A380957 Sorted positions of first appearances in A380955 (sum of prime indices minus sum of distinct prime indices).

1, 4, 8, 16, 27, 64, 81, 243, 256, 529, 729, 961, 1369, 1681, 1849, 2209, 2809, 3481, 3721, 4489, 5041, 5329, 6241, 6889, 7921, 9409, 10201, 10609, 11449, 11881, 12769, 16129, 17161, 18769, 19321, 22201, 22801, 24649, 26569, 27889, 29929, 32041, 32761, 36481

Offset: 1

Author

Gus Wiseman, Feb 13 2025

Keywords

• nonn

Comments

Also appears to be sorted firsts of A374248.

Crossrefs

For length instead of sum we have A151821.

Counting partitions by this statistic (sum minus sum of distinct parts) gives A364916.

Sorted positions of first appearances in A380955.

The unsorted version is A380956.

For product instead of sum we have sorted firsts of A380986.

The multiplicative version is A380988, unsorted A380987, firsts of A290106.

For prime multiplicities instead of prime indices we have A380989, firsts of A380958.

For factors instead of indices we have A381075, see A280286, A280292.

A000040 lists the primes, differences A001223.

A005117 lists squarefree numbers, complement A013929.

A055396 gives least prime index, greatest A061395.

A056239 adds up prime indices, row sums of A112798, counted by A001222.

Cf. A000720, A046660, A071625, A075255, A116861, A136565, A156061, A178503, A175508, A325033, A366528, A366749, A374248.

Programs

Mathematica

prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
q=Table[Total[prix[n]]-Total[Union[prix[n]]],{n,1000}];
Select[Range[Length[q]],FreeQ[Take[q,#-1],q[[#]]]&]