A305613 Numbers whose multiset of prime factors is not knapsack.

30, 60, 70, 72, 84, 90, 120, 140, 144, 150, 168, 180, 210, 216, 240, 252, 270, 280, 286, 288, 300, 308, 330, 336, 350, 360, 378, 390, 420, 432, 440, 450, 480, 490, 495, 504, 510, 525, 528, 540, 560, 570, 572, 576, 588, 594, 600, 616, 630, 646, 648, 660, 672

Offset

1,1

Comments

A multiset of positive integers is knapsack if every distinct submultiset has a different sum.

Links

Table of n, a(n) for n=1..53.

Example

30 = 2 * 3 * 5 is not knapsack because 2 + 3 = 5.

Mathematica

Select[Range[1000], DivisorSigma[0, #]=!=Length[Union[Total/@Subsets[Join@@Cases[FactorInteger[#], {p_, k_}:>Table[p, {k}]]]]]&]

Crossrefs

Cf. A027746, A108917, A122768, A275972, A276024, A299701, A299729, A301855, A301900, A304793, A305611.

Sequence in context: A280011 A175785 A051488 * A267967 A051283 A066031

Adjacent sequences: A305610 A305611 A305612 * A305614 A305615 A305616

Keyword

nonn

Author

Gus Wiseman, Jun 06 2018

Status

approved