cp's OEIS Frontend

A364461 Positive integers such that if prime(a)*prime(b) is a divisor, prime(a+b) is not.

%I A364461 #8 Jul 28 2023 15:54:50
%S A364461 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 A364461 29,31,32,33,34,35,37,38,39,40,41,42,43,44,45,46,47,49,50,51,52,53,54,
%U A364461 55,56,57,58,59,61,62,64,65,66,67,68,69,71,73,74,75,76
%N A364461 Positive integers such that if prime(a)*prime(b) is a divisor, prime(a+b) is not.
%C A364461 Also Heinz numbers of a type of sum-free partitions not allowing re-used parts, counted by A236912.
%e A364461 The prime indices of 198 are {1,2,2,5}, which is sum-free even though it is not knapsack (A299702, A299729), so 198 is in the sequence.
%t A364461 prix[n_]:=If[n==1,{}, Flatten[Cases[FactorInteger[n], {p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A364461 Select[Range[100],Intersection[prix[#], Total/@Subsets[prix[#],{2}]]=={}&]
%Y A364461 Subsets of this type are counted by A085489, with re-usable parts A007865.
%Y A364461 Subsets not of this type are counted by A093971, w/ re-usable parts A088809.
%Y A364461 Partitions of this type are counted by A236912.
%Y A364461 Allowing parts to be re-used gives A364347, counted by A364345.
%Y A364461 The complement allowing parts to be re-used is A364348, counted by A363225.
%Y A364461 The non-binary version allowing re-used parts is counted by A364350.
%Y A364461 The complement is A364462, counted by A237113.
%Y A364461 The non-binary version is A364531, counted by A237667, complement A364532.
%Y A364461 A001222 counts prime indices.
%Y A364461 A108917 counts knapsack partitions, ranks A299702.
%Y A364461 A112798 lists prime indices, sum A056239.
%Y A364461 Cf. A151897, A288728, A320340, A325862, A325864, A326083, A363226, A364346.
%K A364461 nonn
%O A364461 1,2
%A A364461 _Gus Wiseman_, Jul 27 2023