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A325802
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Numbers with one more divisor than distinct subset-sums of their prime indices.
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4
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12, 30, 40, 63, 70, 112, 154, 165, 198, 220, 273, 286, 325, 351, 352, 364, 442, 525, 550, 561, 595, 646, 675, 714, 741, 748, 765, 832, 850, 874, 918, 931, 952, 988, 1045, 1173, 1254, 1334, 1425, 1495, 1539, 1564, 1653, 1666, 1672, 1771, 1794, 1798, 1870, 1900
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OFFSET
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1,1
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COMMENTS
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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. A subset-sum of an integer partition is any sum of a submultiset of it.
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are Heinz numbers of the partitions counted by A325835.
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LINKS
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FORMULA
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EXAMPLE
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The sequence of terms together with their prime indices begins:
12: {1,1,2}
30: {1,2,3}
40: {1,1,1,3}
63: {2,2,4}
70: {1,3,4}
112: {1,1,1,1,4}
154: {1,4,5}
165: {2,3,5}
198: {1,2,2,5}
220: {1,1,3,5}
273: {2,4,6}
286: {1,5,6}
325: {3,3,6}
351: {2,2,2,6}
352: {1,1,1,1,1,5}
364: {1,1,4,6}
442: {1,6,7}
525: {2,3,3,4}
550: {1,3,3,5}
561: {2,5,7}
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MATHEMATICA
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Select[Range[100], DivisorSigma[0, #]==1+Length[Union[hwt/@Divisors[#]]]&]
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CROSSREFS
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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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