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A325795
Numbers with more divisors than the sum of their prime indices.
9
1, 2, 4, 6, 8, 12, 16, 18, 20, 24, 30, 32, 36, 40, 42, 48, 54, 56, 60, 64, 72, 80, 84, 90, 96, 100, 108, 112, 120, 126, 128, 132, 140, 144, 150, 156, 160, 162, 168, 176, 180, 192, 198, 200, 204, 210, 216, 220, 224, 234, 240, 252, 256, 260, 264, 270, 280, 288
OFFSET
1,2
COMMENTS
First differs from A325781 in having 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:
1: {}
2: {1}
4: {1,1}
6: {1,2}
8: {1,1,1}
12: {1,1,2}
16: {1,1,1,1}
18: {1,2,2}
20: {1,1,3}
24: {1,1,1,2}
30: {1,2,3}
32: {1,1,1,1,1}
36: {1,1,2,2}
40: {1,1,1,3}
42: {1,2,4}
48: {1,1,1,1,2}
54: {1,2,2,2}
56: {1,1,1,4}
60: {1,1,2,3}
64: {1,1,1,1,1,1}
MATHEMATICA
Select[Range[100], DivisorSigma[0, #]>Total[Cases[FactorInteger[#], {p_, k_}:>PrimePi[p]*k]]&]
CROSSREFS
Positions of positive terms in A325794.
Heinz numbers of the partitions counted by A325831.
Sequence in context: A174973 A365270 A238443 * A359420 A325781 A231565
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 23 2019
STATUS
approved