cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A360246 Numbers for which the prime indices do not have the same mean as the distinct prime indices.

Original entry on oeis.org

12, 18, 20, 24, 28, 40, 44, 45, 48, 50, 52, 54, 56, 60, 63, 68, 72, 75, 76, 80, 84, 88, 92, 96, 98, 99, 104, 108, 112, 116, 117, 120, 124, 126, 132, 135, 136, 140, 144, 147, 148, 150, 152, 153, 156, 160, 162, 164, 168, 171, 172, 175, 176, 180, 184, 188, 189
Offset: 1

Views

Author

Gus Wiseman, Feb 07 2023

Keywords

Comments

First differs from A242416 in having 126.
Contains no squarefree numbers or perfect powers.
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

Examples

			The terms together with their prime indices begin:
   12: {1,1,2}
   18: {1,2,2}
   20: {1,1,3}
   24: {1,1,1,2}
   28: {1,1,4}
   40: {1,1,1,3}
   44: {1,1,5}
   45: {2,2,3}
   48: {1,1,1,1,2}
   50: {1,3,3}
   52: {1,1,6}
   54: {1,2,2,2}
   56: {1,1,1,4}
   60: {1,1,2,3}
   63: {2,2,4}
   68: {1,1,7}
   72: {1,1,1,2,2}
The prime indices of 126 are {1,2,2,4} with mean 9/4 and distinct prime indices {1,2,4} with mean 7/3, so 126 is in the sequence.

Crossrefs

Signature instead of parts: complement A324570, counted by A114638.
Signature instead of distinct parts: complement A359903, counted by A360068.
These partitions are counted by A360242.
The complement is A360247, counted by A360243.
For median we have A360248, counted by A360244 (complement A360245).
Union of A360252 and A360253, counted by A360250 and A360251.
A058398 counts partitions by mean, also A327482.
A088529/A088530 gives mean of prime signature (A124010).
A112798 lists prime indices, length A001222, sum A056239.
A316413 = numbers whose prime indices have integer mean, distinct A326621.
A326567/A326568 gives mean of prime indices.
A326619/A326620 gives mean of distinct prime indices.
Cf. A000975, A051293, A067340, A067538, A360005, A360241.

Programs

  • Mathematica
    prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[100],Mean[prix[#]]!=Mean[Union[prix[#]]]&]

A360247 Numbers for which the prime indices have the same mean as the distinct prime indices.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 46, 47, 49, 51, 53, 55, 57, 58, 59, 61, 62, 64, 65, 66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 81, 82, 83, 85, 86, 87, 89, 90, 91, 93, 94, 95, 97, 100, 101, 102, 103, 105, 106, 107, 109, 110, 111, 113, 114, 115, 118, 119, 121, 122, 123, 125, 127, 128, 129, 130
Offset: 1

Views

Author

Gus Wiseman, Feb 07 2023

Keywords

Comments

First differs from A072774 in having 90.
First differs from A242414 in lacking 126.
Includes all squarefree numbers and perfect powers.
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

Examples

			The prime indices of 900 are {3,3,2,2,1,1} with mean 2, and the distinct prime indices are {1,2,3} also with mean 2, so 900 is in the sequence.

Crossrefs

Signature instead of parts: A324570, counted by A114638.
Signature instead of distinct parts: A359903, counted by A360068.
These partitions are counted by A360243.
The complement is A360246, counted by A360242.
For median instead of mean the complement is A360248, counted by A360244.
For median instead of mean we have A360249, counted by A360245.
For greater instead of equal mean we have A360252, counted by A360250.
For lesser instead of equal mean we have A360253, counted by A360251.
A008284 counts partitions by number of parts, distinct A116608.
A058398 counts partitions by mean, also A327482.
A088529/A088530 gives mean of prime signature (A124010).
A112798 lists prime indices, length A001222, sum A056239.
A316413 = numbers whose prime indices have integer mean, distinct A326621.
A326567/A326568 gives mean of prime indices.
A326619/A326620 gives mean of distinct prime indices.
Cf. A000975, A051293, A067340, A067538, A360005, A360241.

Programs

  • Maple
    isA360247 := proc(n)
    local ifs,pidx,pe,meanAll,meanDist ;
    if n = 1 then
        return true ;
    end if ;
    ifs := ifactors(n)[2] ;
    # list of prime indices with multiplicity
    pidx := [] ;
    for pe in ifs do
        [numtheory[pi](op(1,pe)),op(2,pe)] ;
        pidx := [op(pidx),%] ;
    end do:
    meanAll := add(op(1,pe)*op(2,pe),pe=pidx) / add(op(2,pe),pe=pidx) ;
    meanDist := add(op(1,pe),pe=pidx) / nops(pidx) ;
    if meanAll = meanDist then
        true;
    else
        false;
    end if;
end proc:
for n from 1 to 130 do
    if isA360247(n) then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, May 22 2023
  • Mathematica
    prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[100],Mean[prix[#]]==Mean[Union[prix[#]]]&]

A360453 Numbers for which the prime multiplicities (or sorted signature) have the same median as the distinct prime indices.

Original entry on oeis.org

1, 2, 9, 12, 18, 40, 100, 112, 125, 180, 250, 252, 300, 352, 360, 392, 396, 405, 450, 468, 504, 540, 588, 600, 612, 675, 684, 720, 756, 792, 828, 832, 882, 900, 936, 1008, 1044, 1116, 1125, 1176, 1188, 1200, 1224, 1332, 1350, 1368, 1372, 1404, 1440, 1452, 1476
Offset: 1

Views

Author

Gus Wiseman, Feb 10 2023

Keywords

Comments

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).

Examples

			The terms together with their prime indices begin:
    1: {}
    2: {1}
    9: {2,2}
   12: {1,1,2}
   18: {1,2,2}
   40: {1,1,1,3}
  100: {1,1,3,3}
  112: {1,1,1,1,4}
  125: {3,3,3}
  180: {1,1,2,2,3}
  250: {1,3,3,3}
  252: {1,1,2,2,4}
  300: {1,1,2,3,3}
  352: {1,1,1,1,1,5}
  360: {1,1,1,2,2,3}
For example, the prime indices of 756 are {1,1,2,2,2,4} with distinct parts {1,2,4} with median 2 and multiplicities {1,2,3} with median 2, so 756 is in the sequence.

Crossrefs

Without taking median we have A109298, unordered A109297.
For mean instead of median we have A324570, counted by A114638.
For indices instead of multiplicities we have A360249, counted by A360245.
For indices instead of distinct indices we have A360454, counted by A360456.
These partitions are counted by A360455.
A088529/A088530 gives mean of prime signature A124010.
A112798 lists prime indices, length A001222, sum A056239.
A240219 counts partitions with mean equal to median, ranks A359889.
A316413 = numbers whose prime indices have integer mean, distinct A326621.
A325347 = partitions with integer median, strict A359907, ranks A359908.
A326567/A326568 gives mean of prime indices.
A326619/A326620 gives mean of distinct prime indices.
A359893 and A359901 count partitions by median.
A360005 gives median of prime indices (times two).
Cf. A000975, A359890, A359903, A360068, A360244, A360247, A360248.

Programs

  • Mathematica
    Select[Range[100],#==1||Median[Last/@FactorInteger[#]]== Median[PrimePi/@First/@FactorInteger[#]]&]

A360249 Numbers for which the prime indices have the same median as the distinct prime indices.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 46, 47, 49, 51, 53, 55, 57, 58, 59, 61, 62, 64, 65, 66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 81, 82, 83, 85, 86, 87, 89, 90, 91, 93, 94, 95, 97, 100, 101, 102, 103, 105, 106, 107, 109, 110, 111, 113, 114, 115, 118, 119, 121, 122, 123, 125, 126, 127, 128, 129, 130
Offset: 1

Views

Author

Gus Wiseman, Feb 07 2023

Keywords

Comments

First differs from A072774 in having 90.
First differs from A242414 in having 180.
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).

Examples

			The prime indices of 126 are {1,2,2,4} with median 2 and distinct prime indices {1,2,4} with median 2, so 126 is in the sequence.
The prime indices of 180 are {1,1,2,2,3} with median 2 and distinct prime indices {1,2,3} with median 2, so 180 is in the sequence.

Crossrefs

These partitions are counted by A360245.
The complement for mean instead of median is A360246, counted by A360242.
For mean instead of median we have A360247, counted by A360243.
The complement is A360248, counted by A360244.
For multiplicities instead of parts: A360453, counted by A360455.
For multiplicities instead of distinct parts: A360454, counted by A360456.
A112798 lists prime indices, length A001222, sum A056239.
A240219 counts partitions with mean equal to median, ranks A359889.
A326567/A326568 gives mean of prime indices.
A326619/A326620 gives mean of distinct prime indices.
A325347 = partitions with integer median, strict A359907, ranks A359908.
A359893 and A359901 count partitions by median.
A359894 = partitions with mean different from median, ranks A359890.
A360005 gives median of prime indices (times two).
Cf. A000975, A078174, A316413, A324570, A359903, A360252, A360253.

Programs

  • Maple
    isA360249 := proc(n)
    local ifs,pidx,pe,medAll,medDist ;
    if n = 1 then
        return true ;
    end if ;
    ifs := ifactors(n)[2] ;
    pidx := [] ;
    for pe in ifs do
        numtheory[pi](op(1,pe)) ;
        pidx := [op(pidx),seq(%,i=1..op(2,pe))] ;
    end do:
    medAll := stats[describe,median](sort(pidx)) ;
    pidx := convert(convert(pidx,set),list) ;
    medDist := stats[describe,median](sort(pidx)) ;
    if medAll = medDist then
        true;
    else
        false;
    end if;
end proc:
for n from 1 to 130 do
    if isA360249(n) then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, May 22 2023
  • Mathematica
    prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[100],Median[prix[#]]==Median[Union[prix[#]]]&]

A360252 Numbers for which the prime indices have greater mean than the distinct prime indices.

Original entry on oeis.org

18, 50, 54, 75, 98, 108, 147, 150, 162, 242, 245, 250, 294, 324, 338, 350, 363, 375, 450, 486, 490, 500, 507, 578, 588, 605, 648, 686, 722, 726, 735, 750, 845, 847, 867, 882, 972, 1014, 1029, 1050, 1058, 1078, 1083, 1125, 1183, 1210, 1250, 1274, 1350, 1372
Offset: 1

Views

Author

Gus Wiseman, Feb 09 2023

Keywords

Comments

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

Examples

			The terms together with their prime indices begin:
    18: {1,2,2}
    50: {1,3,3}
    54: {1,2,2,2}
    75: {2,3,3}
    98: {1,4,4}
   108: {1,1,2,2,2}
   147: {2,4,4}
   150: {1,2,3,3}
   162: {1,2,2,2,2}
   242: {1,5,5}
   245: {3,4,4}
   250: {1,3,3,3}
   294: {1,2,4,4}
   324: {1,1,2,2,2,2}
For example, the prime indices of 350 are {1,3,3,4} with mean 11/4, and the distinct prime indices are {1,3,4} with mean 8/3, so 350 is in the sequence.

Crossrefs

For unequal instead of greater we have A360246, counted by A360242.
For equal instead of greater we have A360247, counted by A360243.
These partitions are counted by A360250.
For less instead of greater we have A360253, counted by A360251.
A112798 lists prime indices, length A001222, sum A056239.
A316413 lists numbers whose indices have integer mean, distinct A326621.
A326567/A326568 gives mean of prime indices.
A326619/A326620 gives mean of distinct prime indices.
Cf. A000975, A051293, A058398, A067340, A067538, A324570, A327482, A359903, A360005, A360241, A360248.

Programs

  • Mathematica
    prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[100],Mean[prix[#]]>Mean[Union[prix[#]]]&]

A360253 Numbers for which the prime indices have lesser mean than the distinct prime indices.

Original entry on oeis.org

12, 20, 24, 28, 40, 44, 45, 48, 52, 56, 60, 63, 68, 72, 76, 80, 84, 88, 92, 96, 99, 104, 112, 116, 117, 120, 124, 126, 132, 135, 136, 140, 144, 148, 152, 153, 156, 160, 164, 168, 171, 172, 175, 176, 180, 184, 188, 189, 192, 198, 200, 204, 207, 208, 212, 220
Offset: 1

Views

Author

Gus Wiseman, Feb 09 2023

Keywords

Comments

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

Examples

			The terms together with their prime indices begin:
   12: {1,1,2}
   20: {1,1,3}
   24: {1,1,1,2}
   28: {1,1,4}
   40: {1,1,1,3}
   44: {1,1,5}
   45: {2,2,3}
   48: {1,1,1,1,2}
   52: {1,1,6}
   56: {1,1,1,4}
   60: {1,1,2,3}
   63: {2,2,4}
   68: {1,1,7}
   72: {1,1,1,2,2}
For example, the prime indices of 350 are {1,3,3,4} with mean 11/4, and the distinct prime indices are {1,3,4} with mean 8/3, so 350 is not in the sequence.

Crossrefs

These partitions are counted by A360251.
For unequal instead of less we have A360246, counted by A360242.
For equal instead of less we have A360247, counted by A360243.
For greater instead of less we have A360252, counted by A360250.
A112798 lists prime indices, length A001222, sum A056239.
A316413 lists numbers whose indices have integer mean, distinct A326621.
A326567/A326568 gives mean of prime indices.
A326619/A326620 gives mean of distinct prime indices.
Cf. A000975, A051293, A058398, A067340, A067538, A324570, A327482, A359903, A360005, A360241, A360248.

Programs

  • Mathematica
    prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[100],Mean[prix[#]]

A360454 Numbers for which the prime multiplicities (or sorted signature) have the same median as the prime indices.

Original entry on oeis.org

1, 2, 9, 54, 100, 120, 125, 135, 168, 180, 189, 240, 252, 264, 280, 297, 300, 312, 336, 351, 396, 408, 440, 450, 456, 459, 468, 480, 513, 520, 528, 540, 552, 560, 588, 612, 616, 621, 624, 672, 680, 684, 696, 728, 744, 756, 760, 783, 816, 828, 837, 880, 882
Offset: 1

Views

Author

Gus Wiseman, Feb 10 2023

Keywords

Comments

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).

Examples

			The terms together with their prime indices begin:
    1: {}
    2: {1}
    9: {2,2}
   54: {1,2,2,2}
  100: {1,1,3,3}
  120: {1,1,1,2,3}
  125: {3,3,3}
  135: {2,2,2,3}
  168: {1,1,1,2,4}
  180: {1,1,2,2,3}
  189: {2,2,2,4}
  240: {1,1,1,1,2,3}
For example, the prime indices of 336 are {1,1,1,1,2,4} with median 1 and multiplicities {1,1,4} with median 1, so 336 is in the sequence.

Crossrefs

For mean instead of median we have A359903, counted by A360068.
For distinct indices instead of indices we have A360453, counted by A360455.
For distinct indices instead of multiplicities: A360249, counted by A360245.
These partitions are counted by A360456.
A088529/A088530 gives mean of prime signature A124010.
A112798 lists prime indices, length A001222, sum A056239.
A240219 counts partitions with mean equal to median, ranked by A359889.
A325347 counts partitions w/ integer median, strict A359907, ranks A359908.
A326567/A326568 gives mean of prime indices.
A326619/A326620 gives mean of distinct prime indices.
A359893 and A359901 count partitions by median.
A359894 counts partitions with mean different from median, ranks A359890.
A360005 gives median of prime indices (times two).
Cf. A000975, A109297, A109298, A114638, A316413, A324570, A360244, A360248.

Programs

  • Mathematica
    prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[1000],Median[prix[#]]==Median[Length/@Split[prix[#]]]&]

A363729 Numbers that are not a power of a prime but whose prime indices satisfy (mean) = (median) = (mode), assuming there is a unique mode.

Original entry on oeis.org

90, 270, 525, 550, 756, 810, 1666, 1911, 1950, 2268, 2430, 2625, 2695, 2700, 2750, 5566, 6762, 6804, 6897, 7128, 7290, 8100, 8500, 9310, 9750, 10285, 10478, 11011, 11550, 11662, 12250, 12375, 12495, 13125, 13377, 13750, 14014, 14703, 18865, 19435, 20412, 21384
Offset: 1

Views

Author

Gus Wiseman, Jun 24 2023

Keywords

Comments

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
A mode in a multiset is an element that appears at least as many times as each of the others. For example, the modes in {a,a,b,b,b,c,d,d,d} are {b,d}.
The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).

Examples

			The prime indices of 6897 are {2,5,5,8}, with mean 5, median 5, and modes {5}, so 6897 is in the sequence.
The terms together with their prime indices begin:
     90: {1,2,2,3}
    270: {1,2,2,2,3}
    525: {2,3,3,4}
    550: {1,3,3,5}
    756: {1,1,2,2,2,4}
    810: {1,2,2,2,2,3}
   1666: {1,4,4,7}
   1911: {2,4,4,6}
   1950: {1,2,3,3,6}
   2268: {1,1,2,2,2,2,4}
   2430: {1,2,2,2,2,2,3}

Crossrefs

For just primes instead of prime powers we have A363722.
Including prime-powers gives A363727, counted by A363719.
These partitions are counted by A363728.
For unequal instead of equal we have A363730, counted by A363720.
A000961 lists the prime powers, complement A024619.
A112798 lists prime indices, length A001222, sum A056239.
A326567/A326568 gives mean of prime indices.
A356862 ranks partitions with a unique mode, counted by A362608.
A359178 ranks partitions with multiple modes, counted by A362610.
A360005 gives twice the median of prime indices.
A362611 counts modes in prime indices, triangle A362614.
A362613 counts co-modes in prime indices, triangle A362615.
A363486 gives least mode in prime indices, A363487 greatest.
Just two statistics:
- (mean) = (median): A359889, counted by A240219.
- (mean) != (median): A359890, counted by A359894.
- (mean) = (mode): counted by A363723, see A363724, A363731.
- (median) = (mode): counted by A363740.
Cf. A215366, A327473, A327476, A359893, A359908, A360009, A360248, A360550, A363721, A363725, A363741.

Programs

  • Mathematica
    prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
modes[ms_]:=Select[Union[ms],Count[ms,#]>=Max@@Length/@Split[ms]&];
Select[Range[1000],!PrimePowerQ[#]&&{Mean[prix[#]]}=={Median[prix[#]]}==modes[prix[#]]&]

A360455 Number of integer partitions of n for which the distinct parts have the same median as the multiplicities.

Original entry on oeis.org

1, 1, 0, 0, 2, 1, 1, 0, 2, 2, 5, 8, 10, 14, 20, 19, 26, 31, 35, 41, 55, 65, 85, 102, 118, 151, 181, 201, 236, 281, 313, 365, 424, 495, 593, 688, 825, 978, 1181, 1374, 1650, 1948, 2323, 2682, 3175, 3680, 4314, 4930, 5718, 6546, 7532, 8557, 9777, 11067, 12622
Offset: 0

Views

Author

Gus Wiseman, Feb 10 2023

Keywords

Comments

The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).

Examples

			The a(1) = 1 through a(11) = 8 partitions:
  1   .  .  22    221   3111   .  3311    333     3331     32222
            211                   41111   32211   33211    33221
                                                  42211    44111
                                                  322111   52211
                                                  511111   322211
                                                           332111
                                                           422111
                                                           3221111

Crossrefs

For mean instead of median: A114638, ranks A324570.
For parts instead of multiplicities: A360245, ranks A360249.
These partitions have ranks A360453.
For parts instead of distinct parts: A360456, ranks A360454.
A000041 counts integer partitions, strict A000009.
A116608 counts partitions by number of distinct parts.
A325347 counts partitions w/ integer median, strict A359907, ranks A359908.
A359893 and A359901 count partitions by median, odd-length A359902.
Cf. A000975, A027193, A240219, A326619/A326620, A359894, A359895, A360068, A360243, A360244, A360248.

Programs

  • Mathematica
    Table[Length[Select[IntegerPartitions[n], Median[Length/@Split[#]]==Median[Union[#]]&]],{n,0,30}]

A361395 Positive integers k such that 2*omega(k) >= bigomega(k).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 73, 74
Offset: 1

Views

Author

Gus Wiseman, Mar 16 2023

Keywords

Comments

Differs from A068938 in having 1 and 4 and lacking 80.
Includes all squarefree numbers.

Examples

			The prime indices of 80 are {1,1,1,1,3}, with 5 parts and 2 distinct parts, and 2*2 < 5, so 80 is not in the sequence.

Crossrefs

Complement of A360558.
Positions of nonnegative terms in A361205.
These partitions are counted by A361394.
A001222 (bigomega) counts prime factors, distinct A001221 (omega).
A112798 lists prime indices, sum A056239.
A360005 gives median of prime indices (times 2), distinct A360457.
Comparing twice the number of distinct parts to the number of parts:
less: A360254, ranks A360558
equal: A239959, ranks A067801
greater: A237365, ranks A361393
less or equal: A237363, ranks A361204
greater or equal: A361394, ranks A361395
Cf. A046660, A061395, A067340, A111907.
Cf. A324515, A324517, A324521, A324560, A324562.
Cf. A360248, A360249, A360454.

Programs

  • Mathematica
    Select[Range[100],2*PrimeNu[#]>=PrimeOmega[#]&]

Formula

A001222(a(n)) <= 2*A001221(a(n)).
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