cp's OEIS Frontend

A380956 Position of first appearance of n in A380955 (sum of prime indices minus sum of distinct prime indices).

%I A380956 #7 Feb 13 2025 18:29:33
%S A380956 1,4,8,16,27,64,81,256,243,529,729,961,1369,1681,1849,2209,2809,3481,
%T A380956 3721,4489,5041,5329,6241,6889,7921,9409,10201,10609,11449,11881,
%U A380956 12769,16129,17161,18769,19321,22201,22801,24649,26569,27889,29929,32041,32761,36481
%N A380956 Position of first appearance of n in A380955 (sum of prime indices minus sum of distinct prime indices).
%C A380956 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.
%C A380956 Also the position of first appearance of n in A374248.
%F A380956 After a(12) = 961, this appears to converge to prime(n)^2.
%e A380956 The terms together with their prime indices begin:
%e A380956      1: {}
%e A380956      4: {1,1}
%e A380956      8: {1,1,1}
%e A380956     16: {1,1,1,1}
%e A380956     27: {2,2,2}
%e A380956     64: {1,1,1,1,1,1}
%e A380956     81: {2,2,2,2}
%e A380956    256: {1,1,1,1,1,1,1,1}
%e A380956    243: {2,2,2,2,2}
%e A380956    529: {9,9}
%e A380956    729: {2,2,2,2,2,2}
%e A380956    961: {11,11}
%e A380956   1369: {12,12}
%e A380956   1681: {13,13}
%e A380956   1849: {14,14}
%e A380956   2209: {15,15}
%t A380956 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A380956 mnrm[s_]:=If[Min@@s==1,mnrm[DeleteCases[s-1,0]]+1,0];
%t A380956 q=Table[Total[prix[n]]-Total[Union[prix[n]]],{n,1000}];
%t A380956 Table[Position[q,k][[1,1]],{k,0,mnrm[q+1]-1}]
%Y A380956 For length instead of sum we have A151821.
%Y A380956 For factors instead of indices we have A280286 (sorted A381075), firsts of A280292.
%Y A380956 Counting partitions by this statistic gives A364916.
%Y A380956 Positions of first appearances in A380955.
%Y A380956 The sorted version is A380957.
%Y A380956 For product instead of sum we have firsts of A380986.
%Y A380956 A multiplicative version is A380987 (sorted A380988), firsts of A290106.
%Y A380956 For prime multiplicities instead of prime indices we have A380989, firsts of A380958.
%Y A380956 A000040 lists the primes, differences A001223.
%Y A380956 A005117 lists squarefree numbers, complement A013929.
%Y A380956 A055396 gives least prime index, greatest A061395.
%Y A380956 A056239 adds up prime indices, row sums of A112798, length A001222.
%Y A380956 A304038 lists distinct prime indices, sum A066328, length A001221.
%Y A380956 Cf. A000720, A046660, A071625, A075255, A116861, A136565, A156061, A178503, A175508, A325033, A366528, A366749, A374248.
%K A380956 nonn
%O A380956 0,2
%A A380956 _Gus Wiseman_, Feb 12 2025