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

Author

Gus Wiseman, May 23 2019

Keywords

• nonn

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).

Examples

			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}
		

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.

Programs

Mathematica

Select[Range[100],DivisorSigma[0,#]<=Total[Cases[FactorInteger[#],{p_,k_}:>PrimePi[p]*k]]&]