A243055 -id:A243055 - cp's OEIS frontend

A359674 Zero-based weighted sum of the prime indices of n in weakly increasing order.

0, 0, 0, 1, 0, 2, 0, 3, 2, 3, 0, 5, 0, 4, 3, 6, 0, 6, 0, 7, 4, 5, 0, 9, 3, 6, 6, 9, 0, 8, 0, 10, 5, 7, 4, 11, 0, 8, 6, 12, 0, 10, 0, 11, 8, 9, 0, 14, 4, 9, 7, 13, 0, 12, 5, 15, 8, 10, 0, 14, 0, 11, 10, 15, 6, 12, 0, 15, 9, 11, 0, 17, 0, 12, 9, 17, 5, 14, 0, 18

Offset: 1

Gus Wiseman, Jan 13 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 zero-based weighted sum of a sequence (y_1,...,y_k) is Sum_{i=1..k} (i-1)*y_i.

			The prime indices of 12 are {1,1,2}, so a(12) = 0*1 + 1*1 + 2*2 = 5.

Positions of last appearances (except 0) are A001248.
Positions of 0's are A008578.
The version for standard compositions is A124757, reverse A231204.
The one-based version is A304818, reverse A318283.
Positions of first appearances are A359675, reverse A359680.
First position of n is A359676(n), reverse A359681.
The reverse version is A359677, firsts A359679.
Number of appearances of positive n is A359678(n).
A053632 counts compositions by zero-based weighted sum.
A112798 lists prime indices, length A001222, sum A056239.
A358136 lists partial sums of prime indices, ranked by A358137, rev A359361.
Cf. A029931, A055932, A243055, A359043, A358194, A359360, A359497, A359681, A359682, A359755.

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
wts[y_]:=Sum[(i-1)*y[[i]],{i,Length[y]}];
Table[wts[primeMS[n]],{n,100}]

A372442 (Greatest binary index of n) minus (greatest prime index of n).

Original entry on oeis.org

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

Offset: 2

Gus Wiseman, May 07 2024

A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793.

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.

For sum instead of maximum we have A372428, zeros A372427.
Positions of zeros are A372436.
For minimum instead of maximum we have A372437, zeros {}.
For length instead of maximum we have A372441, zeros A071814.
Positions of odd terms are A372588, even A372589.
A019565 gives Heinz number of binary indices, adjoint A048675.
A029837 gives greatest binary index, least A001511.
A048793 lists binary indices, length A000120, reverse A272020, sum A029931.
A061395 gives greatest prime index, least A055396.
A070939 gives length of binary expansion.
A112798 lists prime indices, length A001222, reverse A296150, sum A056239.
Cf. A000720, A003963, A014499, A174090, A243055, A355536, A359495, A372429-A372432, A372589-A372591.

bix[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Table[Max[bix[n]]-Max[prix[n]],{n,2,100}]

a(n) = A070939(n) - A061395(n) = A029837(n) - A061395(n) for n > 1.

A241917 If n is a prime with index i, p_i, a(n) = i, (with a(1)=0), otherwise difference (i-j) of the indices of the two largest primes p_i, p_j, i >= j in the prime factorization of n: a(n) = A061395(n) - A061395(A052126(n)).

Original entry on oeis.org

0, 1, 2, 0, 3, 1, 4, 0, 0, 2, 5, 1, 6, 3, 1, 0, 7, 0, 8, 2, 2, 4, 9, 1, 0, 5, 0, 3, 10, 1, 11, 0, 3, 6, 1, 0, 12, 7, 4, 2, 13, 2, 14, 4, 1, 8, 15, 1, 0, 0, 5, 5, 16, 0, 2, 3, 6, 9, 17, 1, 18, 10, 2, 0, 3, 3, 19, 6, 7, 1, 20, 0, 21, 11, 0, 7, 1, 4, 22, 2, 0, 12, 23

Offset: 1

Antti Karttunen, May 13 2014

nonn

Note: the two largest primes in the multiset of prime divisors of n are equal for all numbers that are in A070003, thus, after a(1)=0, A070003 gives the positions of the other zeros in this sequence.

Cf. A052126, A061395, A070003, A122111, A241909.
Cf. A049084, A027746.
Cf. A241919, A242411, A243055 for other variants.

a241917 n = i - j where
            (i:j:_) = map a049084 $ reverse (1 : a027746_row n)
-- Reinhard Zumkeller, May 15 2014

A241917(n) = if(isprime(n), primepi(n), if(1>=omega(n), 0, my(f=factor(n)); if(f[#f~,2]>1, 0, primepi(f[#f~,1])-primepi(f[(#f~)-1,1])))); \\ Antti Karttunen, Jul 10 2024

from sympy import primefactors, primepi
def a061395(n): return 0 if n==1 else primepi(primefactors(n)[-1])
def a052126(n): return 1 if n==1 else n/primefactors(n)[-1]
def a(n): return 0 if n==1 else a061395(n) - a061395(a052126(n)) # Indranil Ghosh, May 19 2017

(define (A241917 n) (- (A061395 n) (A061395 (A052126 n))))

a(n) = A061395(n) - A061395(A052126(n)).

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

A261079 Sum of index differences between prime factors of n, summed over all unordered pairs of primes present (with multiplicity) in the prime factorization of n.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 3, 1, 0, 0, 2, 0, 4, 2, 4, 0, 3, 0, 5, 0, 6, 0, 4, 0, 0, 3, 6, 1, 4, 0, 7, 4, 6, 0, 6, 0, 8, 2, 8, 0, 4, 0, 4, 5, 10, 0, 3, 2, 9, 6, 9, 0, 7, 0, 10, 4, 0, 3, 8, 0, 12, 7, 6, 0, 6, 0, 11, 2, 14, 1, 10, 0, 8, 0, 12, 0, 10, 4, 13, 8, 12, 0, 6, 2, 16, 9, 14, 5, 5, 0, 6, 6, 8, 0, 12, 0, 15, 4, 15, 0, 6, 0, 8, 10, 12, 0, 14, 6, 18, 8, 16, 3, 10

Offset: 1

Antti Karttunen, Sep 23 2015

nonn

			For n = 1 the prime factorization is empty, thus there is nothing to sum, so a(1) = 0.
For n = 6 = 2*3 = prime(1) * prime(2), a(6) = 1 because the (absolute value of) difference between prime indices of 2 and 3 is 1.
For n = 10 = 2*5 = prime(1) * prime(3), a(10) = 2 because the difference between prime indices of 2 and 5 is 2.
For n = 12 = 2*2*3 = prime(1) * prime(1) * prime(2), a(12) = 2 because the difference between prime indices of 2 and 3 is 1, and the pair (2,3) occurs twice as one can pick either one of the two 2's present in the prime factorization to be a pair of a single 3. Note that the index difference between 2 and 2 is 0, thus the pair (2,2) of prime divisors does not contribute to the sum.
For n = 36 = 2*2*3*3, a(36) = 4 because the index difference between 2 and 3 is 1, and the prime factor pair (2,3) occurs 2^2 = four times in total. As the index difference is zero between 2 and 2 as well as between 3 and 3, the pairs (2,2) and (3,3) do not contribute to the sum.

Antti Karttunen, Table of n, a(n) for n = 1..10000
Index entries for sequences computed from indices in prime factorization

Cf. A000720.
Cf. A000961 (positions of zeros), A006094 (positions of ones).
Cf. A243055, A242411.
Cf. also A260737.
A055396 gives minimum prime index, maximum A061395.
A112798 list prime indices, length A001222, sum A056239.
A304818 adds up partial sums of reversed prime indices, row sums of A359361.
A318283 adds up partial sums of prime indices, row sums of A358136.
Cf. A029931, A316413, A325362, A326836, A326844, A355536, A358137, A359362.

Table[Function[p, Total@ Map[Function[b, Times @@ {First@ Differences@ PrimePi@ b, Count[Subsets[p, {2}], c_ /; SameQ[c, b]]}], Subsets[Union@ p, {2}]]][Flatten@ Replace[FactorInteger@ n, {p_, e_} :> ConstantArray[p, e], 2]], {n, 120}] (* Michael De Vlieger, Mar 08 2017 *)

a(n) = A304818(n) - A318283(n). - Gus Wiseman, Jan 09 2023

a(n) = 2*A304818(n) - A359362(n). - Gus Wiseman, Jan 09 2023

A305897 Lexicographically earliest infinite sequence such that a(i) = a(j) => A348717(i) = A348717(j), for all i, j >= 1.

Original entry on oeis.org

1, 2, 2, 3, 2, 4, 2, 5, 3, 6, 2, 7, 2, 8, 4, 9, 2, 10, 2, 11, 6, 12, 2, 13, 3, 14, 5, 15, 2, 16, 2, 17, 8, 18, 4, 19, 2, 20, 12, 21, 2, 22, 2, 23, 7, 24, 2, 25, 3, 26, 14, 27, 2, 28, 6, 29, 18, 30, 2, 31, 2, 32, 11, 33, 8, 34, 2, 35, 20, 36, 2, 37, 2, 38, 10, 39, 4, 40, 2, 41, 9, 42, 2, 43, 12, 44, 24, 45, 2, 46, 6, 47, 30, 48, 14, 49, 2, 50, 15, 51, 2, 52, 2, 53, 16

Offset: 1

Antti Karttunen, Jun 14 2018

nonn

Restricted growth sequence transform of A348717, or equally, of A246277.
Filter sequence for prime factorization patterns, including also information about gaps between prime factors. - Original name, gives the motivation for this sequence. Here the "gaps" refers to differences between the indices of primes present, not the prime gaps as usually understood.
For all i, j:
  A305800(i) = A305800(j) => a(i) = a(j),
  a(i) = a(j) => A077462(i) = A077462(j) => A101296(i) = A101296(j).
  a(i) = a(j) => A243055(i) = A243055(j).

			a(10) = a(21) (= 6) because both have prime exponents [1, 1] and the difference between the prime indices is the same, as 10 = prime(1)*prime(3), and 21 = prime(2)*prime(4).
a(12) != a(18) because the prime exponents [2,1] and [1,2] do not occur in the same order.
a(140) = a(693) (= 71) because both numbers have prime exponents [2, 1, 1] (in this order) and the differences between the indices of the successive prime factors are same: 140 = prime(1)^2 * prime(3) * prime(4), 693 = prime(2)^2 * prime(4) * prime(5).

Antti Karttunen, Table of n, a(n) for n = 1..100000
Index entries for sequences computed from indices in prime factorization

Cf. A077462, A101296, A246277, A300247, A305800, A348717.

Cf. also A286621.

up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A246277(n) = if(1==n, 0, my(f = factor(n), k = primepi(f[1,1])-1); for (i=1, #f~, f[i,1] = prime(primepi(f[i,1])-k)); factorback(f)/2);
v305897 = rgs_transform(vector(up_to,n,A246277(n)));
A305897(n) = v305897[n];

Name changed by Antti Karttunen, Apr 30 2022

A325178 Difference between the length of the minimal square containing and the maximal square contained in the Young diagram of the integer partition with Heinz number n.

Original entry on oeis.org

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

Offset: 1

Gus Wiseman, Apr 08 2019

nonn

The maximal square contained in the Young diagram of an integer partition is called its Durfee square, and its length is the rank of the partition.

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

			The partition (3,3,2,1) has Heinz number 150 and diagram
  o o o
  o o o
  o o
  o
containing maximal square
  o o
  o o
and contained in minimal square
  o o o o
  o o o o
  o o o o
  o o o o
so a(150) = 4 - 2 = 2.

Richard P. Stanley, Enumerative Combinatorics, Volume 2, Cambridge University Press, 1999, p. 289.

Wikipedia, Durfee square.

Positions of zeros are A062457. Positions of 1's are A325179. Positions of 2's are A325180.

Cf. A001222, A046660, A051924, A056239, A061395, A093641, A096771, A115994, A243055, A257990, A263297, A325192, A325195.

durf[n_]:=Length[Select[Range[PrimeOmega[n]],Reverse[Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]][[#]]>=#&]];
codurf[n_]:=If[n==1,0,Max[PrimeOmega[n],PrimePi[FactorInteger[n][[-1,1]]]]];
Table[codurf[n]-durf[n],{n,100}]

a(n) = A263297(n) - A257990(n).

A359676 Least positive integer whose weakly increasing prime indices have zero-based weighted sum n (A359674).

Original entry on oeis.org

1, 4, 6, 8, 14, 12, 16, 20, 30, 24, 32, 36, 40, 52, 48, 56, 100, 72, 80, 92, 96, 104, 112, 124, 136, 148, 176, 152, 214, 172, 184, 188, 262, 212, 272, 236, 248, 244, 304, 268, 346, 284, 328, 292, 386, 316, 398, 332, 376, 356, 458, 388, 478, 404, 472, 412, 526

Offset: 1

Gus Wiseman, Jan 14 2023

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 zero-based weighted sum of a sequence (y_1,...,y_k) is Sum_{i=1..k} (i-1)*y_i.

			The terms together with their prime indices begin:
    1: {}
    4: {1,1}
    6: {1,2}
    8: {1,1,1}
   14: {1,4}
   12: {1,1,2}
   16: {1,1,1,1}
   20: {1,1,3}
   30: {1,2,3}
   24: {1,1,1,2}
   32: {1,1,1,1,1}
   36: {1,1,2,2}
   40: {1,1,1,3}
   52: {1,1,6}
   48: {1,1,1,1,2}

First position of n in A359674, reverse A359677.
The sorted version is A359675, reverse A359680.
The reverse one-based version is A359679, sorted A359754.
The reverse version is A359681.
The one-based version is A359682, sorted A359755.
The version for standard compositions is A359756, one-based A089633.
A053632 counts compositions by zero-based weighted sum.
A112798 lists prime indices, length A001222, sum A056239.
A124757 gives zero-based weighted sum of standard compositions, rev A231204.
A304818 gives weighted sums of prime indices, reverse A318283.
A320387 counts multisets by weighted sum, zero-based A359678.
A358136 lists partial sums of prime indices, ranked by A358137, rev A359361.
Cf. A001248, A029931, A055932, A243055, A359043, A358194, A359497, A359683.

nn=20;
primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
wts[y_]:=Sum[(i-1)*y[[i]],{i,Length[y]}];
seq=Table[wts[primeMS[n]],{n,1,Prime[nn]^2}];
Table[Position[seq,k][[1,1]],{k,0,nn}]

A359677 Zero-based weighted sum of the reversed (weakly decreasing) prime indices of n.

Original entry on oeis.org

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

Offset: 1

Gus Wiseman, Jan 13 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 zero-based weighted sum of a sequence (y_1,...,y_k) is Sum_{i=1..k} (i-1)*y_i.

			The reversed prime indices of 12 are (2,1,1), so a(12) = 0*2 + 1*1 + 2*1 = 3.

Positions of 0's are A008578.
Positions of 1's are A100484.
The version for standard compositions is A231204, reverse of A124757.
The one-based version is A318283, unreversed A304818.
The one-based version for standard compositions is A359042, rev of A029931.
This is the reverse version of A359674.
First position of n is A359679(n), reverse of A359675.
Positions of first appearances are A359680, reverse of A359676.
A053632 counts compositions by weighted sum.
A112798 lists prime indices, length A001222, sum A056239.
A358136 lists partial sums of prime indices, ranked by A358137, rev A359361.
Cf. A001248, A055932, A243055, A359043, A358194, A359678, A359681, A359683, A359754, A359755.

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
wts[y_]:=Sum[(i-1)*y[[i]],{i,Length[y]}];
Table[wts[Reverse[primeMS[n]]],{n,100}]

A359681 Least positive integer whose reversed (weakly decreasing) prime indices have zero-based weighted sum (A359677) equal to n.

Original entry on oeis.org

1, 4, 9, 8, 18, 50, 16, 36, 100, 54, 32, 72, 81, 108, 300, 64, 144, 400, 216, 600, 243, 128, 288, 800, 432, 486, 1350, 648, 256, 576, 729, 864, 2400, 3375, 1296, 3600, 512, 1152, 1944, 1728, 4800, 9000, 2187, 2916, 8100, 1024, 2304, 6400, 3456, 4374, 12150

Offset: 0

Gus Wiseman, Jan 15 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 zero-based weighted sum of a sequence (y_1,...,y_k) is Sum_{i=1..k} (i-1)*y_i.

			The terms together with their prime indices begin:
    1: {}
    4: {1,1}
    9: {2,2}
    8: {1,1,1}
   18: {1,2,2}
   50: {1,3,3}
   16: {1,1,1,1}
   36: {1,1,2,2}
  100: {1,1,3,3}
   54: {1,2,2,2}
   32: {1,1,1,1,1}
   72: {1,1,1,2,2}
   81: {2,2,2,2}
  108: {1,1,2,2,2}
  300: {1,1,2,3,3}

The unreversed version is A359676.
First position of n in A359677, reverse A359674.
The one-based version is A359679, sorted A359754.
The sorted version is A359680, reverse A359675.
The unreversed one-based version is A359682, sorted A359755.
A053632 counts compositions by zero-based weighted sum.
A112798 lists prime indices, length A001222, sum A056239.
A124757 gives zero-based weighted sum of standard compositions, rev A231204.
A304818 gives weighted sum of prime indices, reverse A318283.
A320387 counts multisets by weighted sum, zero-based A359678.
Cf. A001248, A029931, A055932, A089633, A243055, A359043, A358194, A359360, A359361, A359497, A359683.

nn=20;
primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
wts[y_]:=Sum[(i-1)*y[[i]],{i,Length[y]}];
seq=Table[wts[Reverse[primeMS[n]]],{n,1,Prime[nn]^2}];
Table[Position[seq,k][[1,1]],{k,0,nn}]

cp's OEIS Frontend

A359674 Zero-based weighted sum of the prime indices of n in weakly increasing order.

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A372442 (Greatest binary index of n) minus (greatest prime index of n).

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A241917 If n is a prime with index i, p_i, a(n) = i, (with a(1)=0), otherwise difference (i-j) of the indices of the two largest primes p_i, p_j, i >= j in the prime factorization of n: a(n) = A061395(n) - A061395(A052126(n)).

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

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A261079 Sum of index differences between prime factors of n, summed over all unordered pairs of primes present (with multiplicity) in the prime factorization of n.

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A305897 Lexicographically earliest infinite sequence such that a(i) = a(j) => A348717(i) = A348717(j), for all i, j >= 1.

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A325178 Difference between the length of the minimal square containing and the maximal square contained in the Young diagram of the integer partition with Heinz number n.

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A359676 Least positive integer whose weakly increasing prime indices have zero-based weighted sum n (A359674).

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