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A325694
Numbers with one fewer divisors than the sum of their prime indices.
25
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
OFFSET
1,1
COMMENTS
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.
EXAMPLE
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}
MATHEMATICA
Select[Range[1000], DivisorSigma[0, #]==Total[Cases[FactorInteger[#], {p_, k_}:>PrimePi[p]*k]]-1&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 23 2019
STATUS
approved