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

Author

Gus Wiseman, Jun 06 2018

Keywords

• nonn

Comments

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

Examples

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

Crossrefs

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

Programs

Mathematica

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