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 A301899 #7 Apr 08 2018 20:09:46
%S A301899 1,2,3,5,6,7,10,11,13,14,15,17,19,21,22,23,26,29,31,33,34,35,37,38,39,
%T A301899 41,42,43,46,47,51,53,55,57,58,59,61,62,65,66,67,69,71,73,74,77,78,79,
%U A301899 82,83,85,86,87,89,91,93,94,95,97,101,102,103,105,106,107,109
%N A301899 Heinz numbers of strict knapsack partitions. Squarefree numbers such that every divisor has a different Heinz weight A056239(d).
%C A301899 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).
%F A301899 Intersection of A299702 and A005117.
%e A301899 42 is the Heinz number of (4,2,1) which is strict and knapsack, so is in the sequence. 45 is the Heinz number of (3,2,2) which is knapsack but not strict, so is not in the sequence. 30 is the Heinz number of (3,2,1) which is strict but not knapsack, so is not in the sequence.
%e A301899 Sequence of strict knapsack partitions begins: (), (1), (2), (3), (21), (4), (31), (5), (6), (41), (32), (7), (8), (42), (51), (9), (61).
%t A301899 wt[n_]:=If[n===1,0,Total[Cases[FactorInteger[n],{p_,k_}:>k*PrimePi[p]]]];
%t A301899 Select[Range[100],SquareFreeQ[#]&&UnsameQ@@wt/@Divisors[#]&]
%Y A301899 Cf. A000712, A005117, A056239, A108917, A112798, A122768, A275972, A276024, A284640, A296150, A299701, A299702, A299729, A301829, A301854, A301900.
%K A301899 nonn
%O A301899 1,2
%A A301899 _Gus Wiseman_, Mar 28 2018