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A364532
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Positive integers with a prime index equal to the sum of prime indices of some nonprime divisor. Heinz numbers of a variation of sum-full partitions.
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16
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12, 24, 30, 36, 40, 48, 60, 63, 70, 72, 80, 84, 90, 96, 108, 112, 120, 126, 132, 140, 144, 150, 154, 156, 160, 165, 168, 180, 189, 192, 198, 200, 204, 210, 216, 220, 224, 228, 240, 252, 264, 270, 273, 276, 280, 286, 288, 300, 308, 312, 315, 320, 324, 325, 330
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OFFSET
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1,1
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COMMENTS
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First differs from A299729 (non-knapsack) in lacking 525: {2,3,3,4}.
First differs from A325777 in having 462: {1,2,4,5} and lacking 675:{2,2,2,3,3}.
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
These are the Heinz numbers of partitions containing the sum of some non-singleton submultiset.
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LINKS
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EXAMPLE
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The terms together with their prime indices begin:
12: {1,1,2}
24: {1,1,1,2}
30: {1,2,3}
36: {1,1,2,2}
40: {1,1,1,3}
48: {1,1,1,1,2}
60: {1,1,2,3}
63: {2,2,4}
70: {1,3,4}
72: {1,1,1,2,2}
80: {1,1,1,1,3}
84: {1,1,2,4}
90: {1,2,2,3}
96: {1,1,1,1,1,2}
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MATHEMATICA
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Select[Range[100], Intersection[prix[#], Total/@Subsets[prix[#], {2, Length[prix[#]]}]]!={}&]
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CROSSREFS
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A299701 counts distinct subset-sums of prime indices.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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