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A325694
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Numbers with one fewer divisors than the sum of their prime indices.
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25
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5, 9, 14, 15, 44, 45, 50, 78, 104, 105, 110, 135, 196, 225, 272, 276, 342, 380, 405, 476, 572, 585, 608, 650, 693, 726, 735, 825, 888, 930, 968, 1125, 1215, 1218, 1240, 1472, 1476, 1482, 1518, 1566, 1610, 1624, 1976, 1995, 2024, 2090, 2210, 2256, 2565, 2618
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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, with sum A056239(n).
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 A325836.
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LINKS
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EXAMPLE
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The sequence of terms together with their prime indices begins:
5: {3}
9: {2,2}
14: {1,4}
15: {2,3}
44: {1,1,5}
45: {2,2,3}
50: {1,3,3}
78: {1,2,6}
104: {1,1,1,6}
105: {2,3,4}
110: {1,3,5}
135: {2,2,2,3}
196: {1,1,4,4}
225: {2,2,3,3}
272: {1,1,1,1,7}
276: {1,1,2,9}
342: {1,2,2,8}
380: {1,1,3,8}
405: {2,2,2,2,3}
476: {1,1,4,7}
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MATHEMATICA
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Select[Range[1000], DivisorSigma[0, #]==Total[Cases[FactorInteger[#], {p_, k_}:>PrimePi[p]*k]]-1&]
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CROSSREFS
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Cf. A000005, A056239, A112798, A325780, A325792, A325793, A325794, A325795, A325796, A325797, A325798, A325836.
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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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