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A325798
Numbers with at most as many divisors as the sum of their prime indices.
15
3, 5, 7, 9, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 25, 26, 27, 28, 29, 31, 33, 34, 35, 37, 38, 39, 41, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 57, 58, 59, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 85, 86, 87, 88, 89
OFFSET
1,1
COMMENTS
First differs from the complement of A325781 in lacking 156.
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).
EXAMPLE
The sequence of terms together with their prime indices begins:
3: {2}
5: {3}
7: {4}
9: {2,2}
10: {1,3}
11: {5}
13: {6}
14: {1,4}
15: {2,3}
17: {7}
19: {8}
21: {2,4}
22: {1,5}
23: {9}
25: {3,3}
26: {1,6}
27: {2,2,2}
28: {1,1,4}
29: {10}
31: {11}
MATHEMATICA
Select[Range[100], DivisorSigma[0, #]<=Total[Cases[FactorInteger[#], {p_, k_}:>PrimePi[p]*k]]&]
CROSSREFS
Positions of nonpositive terms in A325794.
Heinz numbers of the partitions counted by A325834.
Sequence in context: A067715 A344291 A231564 * A365830 A238524 A237287
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 23 2019
STATUS
approved