A325798 Numbers with at most as many divisors as the sum of their prime indices.

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).

Links

Table of n, a(n) for n=1..66.

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.

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

Cf. A325694, A325780, A325781, A325792, A325793, A325795, A325796, A325797.

Sequence in context: A067715 A344291 A231564 * A365830 A238524 A237287

Adjacent sequences: A325795 A325796 A325797 * A325799 A325800 A325801

Keyword

nonn

Author

Gus Wiseman, May 23 2019

Status

approved