A301900 Heinz numbers of strict non-knapsack partitions. Squarefree numbers such that more than one divisor has the same Heinz weight A056239(d).

30, 70, 154, 165, 210, 273, 286, 330, 390, 442, 462, 510, 546, 561, 570, 595, 646, 690, 714, 741, 770, 858, 870, 874, 910, 930, 1045, 1110, 1122, 1155, 1173, 1190, 1230, 1254, 1290, 1326, 1330, 1334, 1365, 1410, 1430, 1482, 1495, 1590, 1610, 1653, 1770

Offset: 1

Author

Gus Wiseman, Mar 28 2018

Keywords

• nonn

Comments

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).

Examples

			Sequence of strict non-knapsack partitions begins: (321), (431), (541), (532), (4321), (642), (651), (5321), (6321), (761), (5421), (7321), (6421), (752), (8321), (743), (871), (9321), (7421), (862), (5431), (6521).
		

Crossrefs

Cf. A000712, A005117, A056239, A108917, A112798, A122768, A275972, A276024, A284640, A296150, A299701, A299702, A299729, A301829, A301854, A301899.

Programs

Mathematica

wt[n_]:=If[n===1,0,Total[Cases[FactorInteger[n],{p_,k_}:>k*PrimePi[p]]]];
Select[Range[1000],SquareFreeQ[#]&&!UnsameQ@@wt/@Divisors[#]&]

Formula

Complement of A005117 in A299702.