cp's OEIS Frontend

A363261 The partial sums of the prime indices of n include half the sum of all prime indices of n.

%I A363261 #6 Jun 12 2023 08:42:33
%S A363261 4,9,12,16,25,30,40,48,49,63,64,70,81,84,108,112,121,144,154,160,165,
%T A363261 169,192,198,220,256,264,270,273,286,289,325,351,352,360,361,364,390,
%U A363261 442,448,468,480,520,529,561,567,576,595,624,625,640,646,675,714,729
%N A363261 The partial sums of the prime indices of n include half the sum of all prime indices of n.
%C A363261 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.
%e A363261 The terms together with their prime indices begin:
%e A363261    4: {1,1}
%e A363261    9: {2,2}
%e A363261   12: {1,1,2}
%e A363261   16: {1,1,1,1}
%e A363261   25: {3,3}
%e A363261   30: {1,2,3}
%e A363261   40: {1,1,1,3}
%e A363261   48: {1,1,1,1,2}
%e A363261   49: {4,4}
%e A363261   63: {2,2,4}
%e A363261   64: {1,1,1,1,1,1}
%e A363261   70: {1,3,4}
%e A363261   81: {2,2,2,2}
%e A363261   84: {1,1,2,4}
%t A363261 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A363261 Select[Range[100],MemberQ[Accumulate[prix[#]],Total[prix[#]]/2]&]
%Y A363261 Partitions of this type are counted by A322439.
%Y A363261 For parts instead of partial sums we have A344415, counted by A035363.
%Y A363261 A025065 counts palindromic partitions, ranked by A265640.
%Y A363261 A027746 lists prime factors, A112798 indices, length A001222, sum A056239.
%Y A363261 A301987 lists numbers whose sum of prime indices equals their product.
%Y A363261 A322109 ranks partitions of n with no part > n/2, counted by A110618.
%Y A363261 Cf. A001414, A106529, A327473, A327476, A334201, A340387, A360005.
%K A363261 nonn
%O A363261 1,1
%A A363261 _Gus Wiseman_, Jun 06 2023