cp's OEIS Frontend

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

%I A380957 #6 Feb 16 2025 13:36:29
%S A380957 1,4,8,16,27,64,81,243,256,529,729,961,1369,1681,1849,2209,2809,3481,
%T A380957 3721,4489,5041,5329,6241,6889,7921,9409,10201,10609,11449,11881,
%U A380957 12769,16129,17161,18769,19321,22201,22801,24649,26569,27889,29929,32041,32761,36481
%N A380957 Sorted positions of first appearances in A380955 (sum of prime indices minus sum of distinct prime indices).
%C A380957 Also appears to be sorted firsts of A374248.
%t A380957 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A380957 q=Table[Total[prix[n]]-Total[Union[prix[n]]],{n,1000}];
%t A380957 Select[Range[Length[q]],FreeQ[Take[q,#-1],q[[#]]]&]
%Y A380957 For length instead of sum we have A151821.
%Y A380957 Counting partitions by this statistic (sum minus sum of distinct parts) gives A364916.
%Y A380957 Sorted positions of first appearances in A380955.
%Y A380957 The unsorted version is A380956.
%Y A380957 For product instead of sum we have sorted firsts of A380986.
%Y A380957 The multiplicative version is A380988, unsorted A380987, firsts of A290106.
%Y A380957 For prime multiplicities instead of prime indices we have A380989, firsts of A380958.
%Y A380957 For factors instead of indices we have A381075, see A280286, A280292.
%Y A380957 A000040 lists the primes, differences A001223.
%Y A380957 A005117 lists squarefree numbers, complement A013929.
%Y A380957 A055396 gives least prime index, greatest A061395.
%Y A380957 A056239 adds up prime indices, row sums of A112798, counted by A001222.
%Y A380957 Cf. A000720, A046660, A071625, A075255, A116861, A136565, A156061, A178503, A175508, A325033, A366528, A366749, A374248.
%K A380957 nonn
%O A380957 1,2
%A A380957 _Gus Wiseman_, Feb 13 2025