A301900 - OEIS

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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

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OFFSET

1,1

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).

LINKS

Table of n, a(n) for n=1..47.

FORMULA

Complement of A005117 in A299702.

EXAMPLE

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).

MATHEMATICA

wt[n_]:=If[n===1, 0, Total[Cases[FactorInteger[n], {p_, k_}:>k*PrimePi[p]]]];

Select[Range[1000], SquareFreeQ[#]&&!UnsameQ@@wt/@Divisors[#]&]

CROSSREFS

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

Sequence in context: A164596 A295102 A131647 * A357854 A071141 A071312

Adjacent sequences: A301897 A301898 A301899 * A301901 A301902 A301903

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 28 2018

STATUS

approved