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A305613
Numbers whose multiset of prime factors is not knapsack.
1
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.
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}]]]]]&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 06 2018
STATUS
approved