This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A299702 #11 Oct 30 2024 08:05:37
%S A299702 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 A299702 29,31,32,33,34,35,37,38,39,41,42,43,44,45,46,47,49,50,51,52,53,54,55,
%U A299702 56,57,58,59,61,62,64,65,66,67,68,69,71,73,74,75,76,77,78
%N A299702 Heinz numbers of knapsack partitions.
%C A299702 An integer partition is knapsack if every distinct submultiset has a different sum. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%H A299702 Robert Israel, <a href="/A299702/b299702.txt">Table of n, a(n) for n = 1..10000</a>
%p A299702 filter:= proc(n) local F,t,S,i,r;
%p A299702 F:= map(t -> [numtheory:-pi(t[1]),t[2]], ifactors(n)[2]);
%p A299702 S:= {0}: r:= 1;
%p A299702 for t in F do
%p A299702 S:= map(s -> seq(s + i*t[1],i=0..t[2]),S);
%p A299702 r:= r*(t[2]+1);
%p A299702 if nops(S) <> r then return false fi
%p A299702 od;
%p A299702 true
%p A299702 end proc:
%p A299702 select(filter, [$1..100]); # _Robert Israel_, Oct 30 2024
%t A299702 primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A299702 Select[Range[100],UnsameQ@@Plus@@@Union[Rest@Subsets[primeMS[#]]]&]
%Y A299702 Cf. A056239, A108917, A112798, A275972, A276024, A284640, A296150, A299701, A299729.
%K A299702 nonn
%O A299702 1,2
%A A299702 _Gus Wiseman_, Feb 17 2018