A325795 Numbers with more divisors than the sum of their prime indices.

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).

Links

Table of n, a(n) for n=1..58.

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.

Cf. A000005, A002033, A056239, A112798, A299702.

Cf. A325694, A325780, A325781, A325792, A325793, A325796, A325797, A325798.

Sequence in context: A174973 A365270 A238443 * A359420 A325781 A231565

Adjacent sequences: A325792 A325793 A325794 * A325796 A325797 A325798

Keyword

nonn

Author

Gus Wiseman, May 23 2019

Status

approved