A287352 -id:A287352 - cp's OEIS frontend

A355536 Irregular triangle read by rows where row n lists the differences between adjacent prime indices of n; if n is prime, row n is empty.

0, 1, 0, 0, 0, 2, 0, 1, 3, 1, 0, 0, 0, 1, 0, 0, 2, 2, 4, 0, 0, 1, 0, 5, 0, 0, 0, 3, 1, 1, 0, 0, 0, 0, 3, 6, 1, 0, 1, 0, 7, 4, 0, 0, 2, 1, 2, 0, 4, 0, 1, 8, 0, 0, 0, 1, 0, 2, 0, 5, 0, 5, 1, 0, 0, 2, 0, 0, 3, 6, 9, 0, 1, 1, 10, 0, 2, 0, 0, 0, 0, 0, 3, 1, 3, 0, 6

Offset: 2

Gus Wiseman, Jul 12 2022

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 version where zero is prepended to the prime indices is A287352.
One could argue that row n = 1 is empty, but adding it changes only the offset, not the data.

			Triangle begins (showing n, prime indices, differences*):
   2:    (1)       .
   3:    (2)       .
   4:   (1,1)      0
   5:    (3)       .
   6:   (1,2)      1
   7:    (4)       .
   8:  (1,1,1)    0 0
   9:   (2,2)      0
  10:   (1,3)      2
  11:    (5)       .
  12:  (1,1,2)    0 1
  13:    (6)       .
  14:   (1,4)      3
  15:   (2,3)      1
  16: (1,1,1,1)  0 0 0

Gus Wiseman, Sequences counting and ranking integer partitions by the differences of their successive parts.

Row-lengths are A001222 minus one.
The prime indices are A112798, sum A056239.
Row-sums are A243055.
Constant rows have indices A325328.
The Heinz numbers of the rows plus one are A325352.
Strict rows have indices A325368.
Row minima are A355524.
Row maxima are A286470, also A355526.
An adjusted version is A358169, reverse A355534.
Cf. A066312, A124010, A129654, A243056, A287352, A325394, A355523, A355528, A355531.

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Table[Differences[primeMS[n]],{n,2,100}]

A360555 Two times the median of the first differences of the 0-prepended prime indices of n > 1.

Original entry on oeis.org

2, 4, 1, 6, 2, 8, 0, 2, 3, 10, 2, 12, 4, 3, 0, 14, 2, 16, 2, 4, 5, 18, 1, 3, 6, 0, 2, 20, 2, 22, 0, 5, 7, 4, 1, 24, 8, 6, 1, 26, 2, 28, 2, 2, 9, 30, 0, 4, 2, 7, 2, 32, 1, 5, 1, 8, 10, 34, 2, 36, 11, 4, 0, 6, 2, 38, 2, 9, 2, 40, 0, 42, 12, 2, 2, 5, 2, 44, 0, 0

Offset: 2

Gus Wiseman, Feb 14 2023

nonn

The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length). Since the denominator is always 1 or 2, the median can be represented as an integer by multiplying by 2.

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 0-prepended prime indices of 1617 are {0,2,4,4,5}, with sorted differences {0,1,2,2}, with median 3/2, so a(1617) = 3.

The version for divisors is A063655.
Differences of 0-prepended prime indices are listed by A287352.
The version for prime indices is A360005.
The version for distinct prime indices is A360457.
The version for distinct prime factors is A360458.
The version for prime factors is A360459.
The version for prime multiplicities is A360460.
Positions of even terms are A360556
Positions of odd terms are A360557
Positions of 0's are A360558, counted by A360254.
For mean instead of two times median we have A360614/A360615.
A112798 lists prime indices, length A001222, sum A056239.
A325347 counts partitions with integer median, complement A307683.
A326567/A326568 gives mean of prime indices.
A359893 and A359901 count partitions by median, odd-length A359902.
Cf. A000975, A026424, A359907, A359908, A359912, A360550.

prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Table[2*Median[Differences[Prepend[prix[n],0]]],{n,2,100}]

A355534 Irregular triangle read by rows where row n lists the augmented differences of the reversed prime indices of n.

Original entry on oeis.org

1, 2, 1, 1, 3, 2, 1, 4, 1, 1, 1, 1, 2, 3, 1, 5, 2, 1, 1, 6, 4, 1, 2, 2, 1, 1, 1, 1, 7, 1, 2, 1, 8, 3, 1, 1, 3, 2, 5, 1, 9, 2, 1, 1, 1, 1, 3, 6, 1, 1, 1, 2, 4, 1, 1, 10, 2, 2, 1, 11, 1, 1, 1, 1, 1, 4, 2, 7, 1, 2, 3, 1, 2, 1, 1, 12, 8, 1, 5, 2, 3, 1, 1, 1

Offset: 2

Gus Wiseman, Jul 12 2022

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 augmented differences aug(q) of a (usually weakly decreasing) sequence q of length k are given by aug(q)i = q_i - q{i+1} + 1 if i < k and aug(q)_k = q_k. For example, we have aug(6,5,5,3,3,3) = (2,1,3,1,1,3).
One could argue that row n = 1 is empty, but adding it changes only the offset, not the data.

			Triangle begins:
   2: 1
   3: 2
   4: 1 1
   5: 3
   6: 2 1
   7: 4
   8: 1 1 1
   9: 1 2
  10: 3 1
  11: 5
  12: 2 1 1
  13: 6
  14: 4 1
  15: 2 2
  16: 1 1 1 1
For example, the reversed prime indices of 825 are (5,3,3,2), which have augmented differences (3,1,2,2).

Gus Wiseman, Sequences counting and ranking integer partitions by the differences of their successive parts.

Crossrefs found in the link are not repeated here.
Row-lengths are A001222.
Row-sums are A252464
Other similar triangles are A287352, A091602.
Constant rows have indices A307824.
The Heinz numbers of the rows are A325351.
Strict rows have indices A325366.
Row minima are A355531, non-augmented A355524, also A355525.
Row maxima are A355535, non-augmented A286470, also A355526.
The non-augmented version is A355536, also A355533.
A112798 lists prime indices, sum A056239.
Cf. A066312, A124010, A129654, A243055, A243056, A325352, A325394, A355523, A355528, A355531.

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
aug[y_]:=Table[If[i

A253566 Permutation of natural numbers: a(n) = A243071(A122111(n)).

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 8, 7, 5, 12, 16, 14, 32, 24, 10, 15, 64, 13, 128, 28, 20, 48, 256, 30, 9, 96, 11, 56, 512, 26, 1024, 31, 40, 192, 18, 29, 2048, 384, 80, 60, 4096, 52, 8192, 112, 22, 768, 16384, 62, 17, 25, 160, 224, 32768, 27, 36, 120, 320, 1536, 65536, 58, 131072, 3072, 44, 63, 72, 104, 262144, 448, 640, 50, 524288, 61, 1048576, 6144, 21

Offset: 1

Antti Karttunen, Jan 03 2015

nonn

Note the indexing: domain starts from one, while the range includes also zero. See also comments in A253564.

The a(n)-th composition in standard order (graded reverse-lexicographic, A066099) is one plus the first differences of the weakly increasing sequence of prime indices of n with 1 prepended. See formula for a simplification. The triangular form is A358169. The inverse is A253565. Not prepending 1 gives A358171. For Heinz numbers instead of standard compositions we have A325351 (without prepending A325352). - Gus Wiseman, Dec 23 2022

			From _Gus Wiseman_, Dec 23 2022: (Start)
This represents the following bijection between partitions and compositions. The reversed prime indices of n together with the a(n)-th composition in standard order are:
   1:        () -> ()
   2:       (1) -> (1)
   3:       (2) -> (2)
   4:     (1,1) -> (1,1)
   5:       (3) -> (3)
   6:     (2,1) -> (1,2)
   7:       (4) -> (4)
   8:   (1,1,1) -> (1,1,1)
   9:     (2,2) -> (2,1)
  10:     (3,1) -> (1,3)
  11:       (5) -> (5)
  12:   (2,1,1) -> (1,1,2)
  13:       (6) -> (6)
  14:     (4,1) -> (1,4)
  15:     (3,2) -> (2,2)
  16: (1,1,1,1) -> (1,1,1,1)
(End)

Antti Karttunen, Table of n, a(n) for n = 1..1024
Index entries for sequences that are permutations of the natural numbers

Inverse: A253565.
Cf. A122111, A243071, A253564, A054429, A336120, A336125.
Applying A000120 gives A001222.
A reverse version is A156552, inverse essentially A005940.
The inverse is A253565, triangular form A242628.
The triangular form is A358169.
A048793 gives partial sums of reversed standard comps, Heinz number A019565.
A066099 lists standard compositions, lengths A000120, sums A070939.
A112798 list prime indices, sum A056239.
A358134 gives partial sums of standard compositions, Heinz number A358170.
Cf. A029837, A241916, A243055, A287352, A325390, A355534, A358171, A359042.

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
stcinv[q_]:=Total[2^(Accumulate[Reverse[q]])]/2;
stcinv/@Table[Differences[Prepend[primeMS[n],1]]+1,{n,100}] (* Gus Wiseman, Dec 23 2022 *)

(define (A253566 n) (A243071 (A122111 n)))

a(n) = A243071(A122111(n)).
As a composition of other permutations:
a(n) = A054429(A253564(n)).
a(n) = A336120(n) + A336125(n). - Antti Karttunen, Jul 18 2020
If 2n = Product_{i=1..k} prime(x_i) then a(n) = Sum_{i=1..k-1} 2^(x_k-x_{k-i}+i-1). - Gus Wiseman, Dec 23 2022

A036913 Sparsely totient numbers; numbers n such that m > n implies phi(m) > phi(n).

Original entry on oeis.org

2, 6, 12, 18, 30, 42, 60, 66, 90, 120, 126, 150, 210, 240, 270, 330, 420, 462, 510, 630, 660, 690, 840, 870, 1050, 1260, 1320, 1470, 1680, 1890, 2310, 2730, 2940, 3150, 3570, 3990, 4620, 4830, 5460, 5610, 5670, 6090, 6930, 7140, 7350, 8190, 9240, 9660

Offset: 1

David W. Wilson

nonn

The paper by Masser and Shiu lists 150 terms of this sequence less than 10^6. For odd prime p, they show that p# and p*p# are in this sequence, where p# denotes the primorial (A002110). - T. D. Noe, Jun 14 2006

Conjecture: Except for 2 and 18, all terms are Zumkeller numbers (A083207). Verified for the first 1800 terms. - Ivan N. Ianakiev, Sep 04 2022

			This sequence contains 60 because of all the numbers whose totient is <=16, 60 is the largest such number. [From _Graeme McRae_, Feb 12 2009]
From _Michael De Vlieger_, Jun 25 2017: (Start)
Positions of primorials A002110(k) in a(n):
     n     k       a(n) = A002110(k)
  ----------------------------------
     1     1                       2
     2     2                       6
     5     3                      30
    13     4                     210
    31     5                    2310
    69     6                   30030
   136     7                  510510
   231     8                 9699690
   374     9               223092870
   578    10              6469693230
   836    11            200560490130
  1169    12           7420738134810
  1591    13         304250263527210
  2149    14       13082761331670030
  2831    15      614889782588491410
  3667    16    32589158477190044730
  4661    17  1922760350154212639070
(End)

T. D. Noe, Table of n, a(n) for n = 1..5000
Roger C. Baker and Glyn Harman, Sparsely totient numbers, Annales de la Faculté des Sciences de Toulouse Ser. 6, 5 no. 2 (1996), 183-190.
Glyn Harman, On sparsely totient numbers, Glasgow Math. J. 33 (1991), 349-358.
D. W. Masser and P. Shiu, On sparsely totient numbers, Pacific J. Math. 121, no. 2 (1986), 407-426.
Michael De Vlieger, Largest k such that A002110(k) | a(n) and A287352(a(n)).
Michael De Vlieger, First term m > prime(n)^2 in A036913 such that gcd(prime(n), m) = 1.

Cf. A097942 (highly totient numbers). Records in A006511 (see also A132154).

nn=10000; lastN=Table[0,{nn}]; Do[e=EulerPhi[n]; If[e<=nn, lastN[[e]]=n], {n,10nn}]; mx=0; lst={}; Do[If[lastN[[i]]>mx, mx=lastN[[i]]; AppendTo[lst,mx]], {i,Length[lastN]}]; lst (* T. D. Noe, Jun 14 2006 *)

A355524 Minimal difference between adjacent prime indices of n > 1, or 0 if n is prime.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 3, 1, 0, 0, 0, 0, 0, 2, 4, 0, 0, 0, 5, 0, 0, 0, 1, 0, 0, 3, 6, 1, 0, 0, 7, 4, 0, 0, 1, 0, 0, 0, 8, 0, 0, 0, 0, 5, 0, 0, 0, 2, 0, 6, 9, 0, 0, 0, 10, 0, 0, 3, 1, 0, 0, 7, 1, 0, 0, 0, 11, 0, 0, 1, 1, 0, 0, 0, 12, 0, 0, 4, 13, 8

Offset: 2

Gus Wiseman, Jul 10 2022

nonn

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 prime indices of 9842 are {1,4,8,12}, with differences (3,4,4), so a(9842) = 3.

Gus Wiseman, Sequences counting and ranking integer partitions by the differences of their successive parts.

Crossrefs found in the link are not repeated here.
Positions of first appearances are A077017 w/o the first term.
Positions of terms > 0 are A120944.
Positions of zeros are A130091.
Triangle A238353 counts m such that A056239(m) = n and a(m) = k.
For maximal difference we have A286470 or A355526.
Positions of terms > 1 are A325161.
If singletons (k) have minimal difference k we get A355525.
Positions of 1's are A355527.
Prepending 0 to the prime indices gives A355528.
A115720 and A115994 count partitions by their Durfee square.
A287352, A355533, A355534, A355536 list the differences of prime indices.
Cf. A000005, A066312, A238354, A238710, A286469, A351294, A352822, A355530, A355531, A355532.

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Table[If[PrimeQ[n],0,Min@@Differences[primeMS[n]]],{n,2,100}]

A360557 Numbers > 1 whose sorted first differences of 0-prepended prime indices have non-integer median.

Original entry on oeis.org

4, 10, 15, 22, 24, 25, 33, 34, 36, 40, 46, 51, 54, 55, 56, 62, 69, 77, 82, 85, 88, 93, 94, 100, 104, 115, 118, 119, 121, 123, 134, 135, 136, 141, 146, 152, 155, 161, 166, 177, 184, 187, 194, 196, 201, 205, 206, 217, 218, 219, 220, 221, 225, 232, 235, 240, 248

Offset: 1

Gus Wiseman, Feb 17 2023

nonn

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).

			The 0-prepended prime indices of 1617 are {0,2,4,4,5}, with sorted differences {0,1,2,2}, with median 3/2, so 1617 is in the sequence.

For mean instead of median complement we have A340610, counted by A168659.
For mean instead of median we have A360668, counted by A200727.
Positions of odd terms in A360555.
The complement is A360556 (without 1), counted by A360688.
These partitions are counted by A360691.
- For divisors (A063655) we have A139710, complement A139711.
- For prime indices (A360005) we have A359912, complement A359908.
- For distinct prime indices (A360457) we have A360551, complement A360550.
- For distinct prime factors (A360458) we have A100367, complement A360552.
- For prime factors (A360459) we have A072978, complement A359913.
- For prime multiplicities (A360460) we have A360554, complement A360553.
- For 0-prepended differences (A360555) we have A360557, complement A360556.
A112798 lists prime indices, length A001222, sum A056239.
A287352 lists 0-prepended first differences of prime indices.
A325347 counts partitions with integer median, complement A307683.
A355536 lists first differences of prime indices.
A359893 and A359901 count partitions by median, odd-length A359902.
A360614/A360615 = mean of first differences of 0-prepended prime indices.
Cf. A000975, A026424, A078175, A316413, A360009, A360558, A360669, A360681.

prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[2,100],!IntegerQ[Median[Differences[Prepend[prix[#],0]]]]&]

A355526 Maximal difference between adjacent prime indices of n, or k if n is the k-th prime.

Original entry on oeis.org

1, 2, 0, 3, 1, 4, 0, 0, 2, 5, 1, 6, 3, 1, 0, 7, 1, 8, 2, 2, 4, 9, 1, 0, 5, 0, 3, 10, 1, 11, 0, 3, 6, 1, 1, 12, 7, 4, 2, 13, 2, 14, 4, 1, 8, 15, 1, 0, 2, 5, 5, 16, 1, 2, 3, 6, 9, 17, 1, 18, 10, 2, 0, 3, 3, 19, 6, 7, 2, 20, 1, 21, 11, 1, 7, 1, 4, 22, 2, 0, 12

Offset: 2

Gus Wiseman, Jul 10 2022

nonn

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 prime indices of 9842 are {1,4,8,12}, with differences (3,4,4), so a(9842) = 4.

Gus Wiseman, Sequences counting and ranking integer partitions by the differences of their successive parts.

Crossrefs found in the link are not repeated here.
Positions of first appearances are 4 followed by A000040.
Positions of 0's are A025475, minimal version A013929.
Positions of 1's are 2 followed by A066312, minimal version A355527.
Triangle A238710 counts m such that A056239(m) = n and a(m) = k.
Prepending 0 to the prime indices gives A286469, minimal version A355528.
See also A286470, minimal version A355524.
The minimal version is A355525, triangle A238709.
The augmented version is A355532.
A001522 counts partitions with a fixed point (unproved), ranked by A352827.
A287352, A355533, A355534, A355536 list the differences of prime indices.
Cf. A000005, A047966, A091602, A238353, A279945, A325160, A325161, A352822, A351294, A355530.

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Table[If[PrimeQ[n],PrimePi[n],Max@@Differences[primeMS[n]]],{n,2,100}]

A355525 Minimal difference between adjacent prime indices of n, or k if n is the k-th prime.

Original entry on oeis.org

1, 2, 0, 3, 1, 4, 0, 0, 2, 5, 0, 6, 3, 1, 0, 7, 0, 8, 0, 2, 4, 9, 0, 0, 5, 0, 0, 10, 1, 11, 0, 3, 6, 1, 0, 12, 7, 4, 0, 13, 1, 14, 0, 0, 8, 15, 0, 0, 0, 5, 0, 16, 0, 2, 0, 6, 9, 17, 0, 18, 10, 0, 0, 3, 1, 19, 0, 7, 1, 20, 0, 21, 11, 0, 0, 1, 1, 22, 0, 0, 12

Offset: 2

Gus Wiseman, Jul 10 2022

nonn

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 prime indices of 9842 are {1,4,8,12}, with differences (3,4,4), so a(9842) = 3.

Gus Wiseman, Sequences counting and ranking integer partitions by the differences of their successive parts.

Crossrefs found in the link are not repeated here.
Positions of first appearances are 4 followed by A000040.
Positions of 0's are A013929, see also A130091.
Triangle A238709 counts m such that A056239(m) = n and a(m) = k.
For maximal instead of minimal difference we have A286470.
Positions of terms > 1 are A325160, also A325161.
See also A355524, A355528.
Positions of 1's are A355527.
A001522 counts partitions with a fixed point (unproved), ranked by A352827.
A238352 counts partitions by fixed points, rank statistic A352822.
A287352, A355533, A355534, A355536 list the differences of prime indices.
Cf. A066312, A120944, A238353, A279945, A286469, A325351, A325352, A351294, A355526, A355530, A355531, A355532.

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Table[If[PrimeQ[n],PrimePi[n],Min@@Differences[primeMS[n]]],{n,2,100}]

A355533 Irregular triangle read by rows where row n lists the differences between adjacent prime indices of n; if n is prime(k), then row n is just (k).

Original entry on oeis.org

1, 2, 0, 3, 1, 4, 0, 0, 0, 2, 5, 0, 1, 6, 3, 1, 0, 0, 0, 7, 1, 0, 8, 0, 2, 2, 4, 9, 0, 0, 1, 0, 5, 0, 0, 0, 3, 10, 1, 1, 11, 0, 0, 0, 0, 3, 6, 1, 0, 1, 0, 12, 7, 4, 0, 0, 2, 13, 1, 2, 14, 0, 4, 0, 1, 8, 15, 0, 0, 0, 1, 0, 2, 0

Offset: 2

Gus Wiseman, Jul 12 2022

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 version where zero is prepended to the prime indices before taking differences is A287352.
One could argue that row n = 1 is empty, but adding it changes only the offset, with no effect on the data.

			Triangle begins (showing n, prime indices, differences*):
   2:    (1)       1
   3:    (2)       2
   4:   (1,1)      0
   5:    (3)       3
   6:   (1,2)      1
   7:    (4)       4
   8:  (1,1,1)    0 0
   9:   (2,2)      0
  10:   (1,3)      2
  11:    (5)       5
  12:  (1,1,2)    0 1
  13:    (6)       6
  14:   (1,4)      3
  15:   (2,3)      1
  16: (1,1,1,1)  0 0 0
For example, the prime indices of 24 are (1,1,1,2), with differences (0,0,1).

Gus Wiseman, Sequences counting and ranking integer partitions by the differences of their successive parts.

Crossrefs found in the link are not repeated here.
Row sums are A243056.
The version for prime indices prepended by 0 is A287352.
Constant rows have indices A325328.
Strict rows have indices A325368.
Number of distinct terms in each row are 1 if prime, otherwise A355523.
Row minima are A355525, augmented A355531.
Row maxima are A355526, augmented A355535.
The augmented version is A355534, Heinz number A325351.
The version with prime-indexed rows empty is A355536, Heinz number A325352.
A112798 lists prime indices, sum A056239.
Cf. A001222, A066312, A124010, A286469, A286470, A325160, A325390, A355524.

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Table[If[PrimeQ[n],{PrimePi[n]},Differences[primeMS[n]]],{n,2,30}]

Row lengths are 1 or A001222(n) - 1 depending on whether n is prime.

cp's OEIS Frontend

A355536 Irregular triangle read by rows where row n lists the differences between adjacent prime indices of n; if n is prime, row n is empty.

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A360555 Two times the median of the first differences of the 0-prepended prime indices of n > 1.

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A355534 Irregular triangle read by rows where row n lists the augmented differences of the reversed prime indices of n.

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A253566 Permutation of natural numbers: a(n) = A243071(A122111(n)).

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A036913 Sparsely totient numbers; numbers n such that m > n implies phi(m) > phi(n).

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A355524 Minimal difference between adjacent prime indices of n > 1, or 0 if n is prime.

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A360557 Numbers > 1 whose sorted first differences of 0-prepended prime indices have non-integer median.

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A355526 Maximal difference between adjacent prime indices of n, or k if n is the k-th prime.

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