A074827 -id:A074827 - cp's OEIS frontend

A322839 Numbers n with more prime factors (counted with multiplicity) than n+1.

4, 6, 8, 10, 12, 16, 18, 20, 22, 24, 28, 30, 32, 36, 40, 42, 45, 46, 48, 50, 52, 54, 56, 58, 60, 64, 66, 68, 70, 72, 76, 78, 80, 81, 82, 84, 88, 90, 92, 96, 100, 102, 104, 105, 106, 108, 110, 112, 114, 117, 120, 126, 128, 130, 132, 136, 138, 140, 144, 148, 150

Offset: 1

Gus Wiseman, Dec 28 2018

nonn

First differs from A074827 in having 104.

			104 has four prime factors (2, 2, 2, 13), while 105 has only three (3, 5, 7), so 104 belongs to the sequence.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000961, A001221, A001222, A045920, A294277, A294278, A302242, A322838, A322840.

R:= NULL: count:= 0: w:= 0:
for n from 2 while count < 100 do
  v:= numtheory:-bigomega(n);
  if v < w then R:= R,n-1; count:= count+1; fi;
  w:= v;
od:
R; # Robert Israel, Jan 16 2023

Select[Range[100],PrimeOmega[#]>PrimeOmega[#+1]&]
Position[Partition[PrimeOmega[Range[200]],2,1],?(#[[1]]>#[[2]]&),1,Heads -> False]//Flatten (* _Harvey P. Dale, Jan 02 2021 *)

A364718 Numbers k such that d(k) > d(k+1) > d(k+2), where d(n) is the number of divisors of n.

Original entry on oeis.org

45, 80, 81, 105, 165, 224, 225, 260, 261, 272, 315, 324, 345, 357, 384, 405, 435, 440, 441, 464, 465, 476, 477, 495, 512, 555, 560, 561, 567, 585, 594, 595, 620, 624, 627, 650, 651, 675, 704, 714, 715, 795, 800, 825, 836, 837, 855, 860, 861, 884, 885, 891, 896, 915

Offset: 1

Seiichi Manyama, Aug 04 2023

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Cf. A000005, A075029, A364657.

Cf. A074827, A364719, A364720.

isok(n) = numdiv(n)>numdiv(n+1) && numdiv(n+1)>numdiv(n+2);

A364719 Numbers k such that d(k) > d(k+1) > d(k+2) > d(k+3), where d(n) is the number of divisors of n.

Original entry on oeis.org

80, 224, 260, 440, 464, 476, 560, 594, 650, 714, 836, 860, 884, 980, 1016, 1088, 1184, 1280, 1376, 1520, 1700, 1862, 1904, 2024, 2060, 2096, 2444, 2450, 2816, 2870, 2960, 2996, 3020, 3024, 3164, 3200, 3320, 3380, 3450, 3620, 3800, 3944, 3968, 4004, 4130, 4136, 4250

Offset: 1

Seiichi Manyama, Aug 04 2023

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Cf. A000005, A050944, A075029.

Cf. A074827, A364718, A364720.

Flatten@Position[Differences@#&/@Partition[DivisorSigma[0,Range@5000],4,1], {?(#<0&)..}] (* _Hans Rudolf Widmer, Mar 11 2024 *)

isok(n) = numdiv(n)>numdiv(n+1) && numdiv(n+1)>numdiv(n+2) && numdiv(n+2)>numdiv(n+3);

A364720 Numbers k such that d(k) > d(k+1) > d(k+2) > d(k+3) > d(k+4), where d(n) is the number of divisors of n.

Original entry on oeis.org

28974, 28975, 39150, 39444, 39445, 44863, 60775, 64015, 68875, 71995, 75174, 79135, 79848, 79849, 91195, 103615, 113904, 113905, 118825, 126294, 141955, 143143, 148974, 149823, 150955, 154375, 160734, 160735, 160974, 161343, 167824, 171925, 177330, 181194, 181195

Offset: 1

Seiichi Manyama, Aug 04 2023

Seiichi Manyama, Table of n, a(n) for n = 1..1000

Cf. A000005, A075029.

Cf. A074827, A364718, A364719.

Flatten@Position[Differences@# &/@Partition[DivisorSigma[0, Range@1000000],5,1], {?(# < 0 &) ..}] (* _Hans Rudolf Widmer, Mar 11 2024 *)

isok(n) = numdiv(n)>numdiv(n+1) && numdiv(n+1)>numdiv(n+2) && numdiv(n+2)>numdiv(n+3) && numdiv(n+3)>numdiv(n+4);

A074709 Base 4 expansion of 1/n has equal percentage of each digit 0,1,2,3.

Original entry on oeis.org

34, 194, 578, 866, 1889, 2017, 2434, 2722, 2897, 4993, 7393, 7394, 7841, 9826, 10562, 10882, 11777, 11969, 15074, 16993, 17282, 18818, 20129, 20417, 20849, 23041, 24322, 35426, 40193, 40289

Offset: 1

Donald S. McDonald, Sep 04 2002

Robert Israel, Table of n, a(n) for n = 1..252

Cf. A073761, A074827, A074900.

filter:= proc(n) local m,L,i;
  if n mod 4 = 0 then return false fi;
  if n::odd then
    m:= numtheory:-order(4,n);
    if m mod 4 <> 0 then return false fi;
    L:= convert(4^m+(4^m-1)/n,base,4)[1..m];
  else
    m:= numtheory:-order(4,n/2);
    if m mod 4 <> 0 then return false fi;
    L:= convert(4^m + 4*(4^m-1)/n,base,4)[1..m];
  fi;
  nops({seq(numboccur(i,L),i=0..3)}) = 1
end proc:
select(filter, [$3..10^5]); # Robert Israel, Dec 28 2020

Corrected and extended by Robert G. Wilson v, Sep 06 2002

cp's OEIS Frontend

A322839 Numbers n with more prime factors (counted with multiplicity) than n+1.

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A364718 Numbers k such that d(k) > d(k+1) > d(k+2), where d(n) is the number of divisors of n.

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A364719 Numbers k such that d(k) > d(k+1) > d(k+2) > d(k+3), where d(n) is the number of divisors of n.

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A364720 Numbers k such that d(k) > d(k+1) > d(k+2) > d(k+3) > d(k+4), where d(n) is the number of divisors of n.

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A074709 Base 4 expansion of 1/n has equal percentage of each digit 0,1,2,3.

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