cp's OEIS Frontend

A364531 Positive integers with no prime index equal to the sum of prime indices of any nonprime divisor.

%I A364531 #7 Aug 03 2023 09:04:19
%S A364531 1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,18,19,20,21,22,23,25,26,27,28,
%T A364531 29,31,32,33,34,35,37,38,39,41,42,43,44,45,46,47,49,50,51,52,53,54,55,
%U A364531 56,57,58,59,61,62,64,65,66,67,68,69,71,73,74,75,76,77
%N A364531 Positive integers with no prime index equal to the sum of prime indices of any nonprime divisor.
%C A364531 First differs from A299702 (knapsack) in having 525: {2,3,3,4}.
%C A364531 First differs from A325778 in lacking 462: {1,2,4,5}.
%C A364531 These are the Heinz numbers of partitions whose parts are disjoint from their own non-singleton subset-sums.
%t A364531 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A364531 Select[Range[100],Intersection[prix[#],Total/@Subsets[prix[#],{2,Length[prix[#]]}]]=={}&]
%Y A364531 Partitions of this type are counted by A237667, strict A364349.
%Y A364531 The binary version is A364462, complement A364461.
%Y A364531 The complement is A364532, counted by A237668.
%Y A364531 A000005 counts divisors, nonprime A033273, composite A055212.
%Y A364531 A299701 counts distinct subset-sums of prime indices.
%Y A364531 A299702 ranks knapsack partitions, counted by A108917, complement A299729.
%Y A364531 A363260 counts partitions disjoint from differences, complement A364467.
%Y A364531 Cf. A002865, A236912, A237113, A320340, A326083, A363225, A364347.
%K A364531 nonn
%O A364531 1,2
%A A364531 _Gus Wiseman_, Aug 01 2023