A325797 Numbers with fewer divisors than the sum of their prime indices.

5, 7, 9, 11, 13, 14, 15, 17, 19, 21, 22, 23, 25, 26, 27, 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, 67, 68, 69, 71, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 85, 86, 87, 89, 91, 92, 93, 94, 95, 97

Offset: 1

Author

Gus Wiseman, May 23 2019

Keywords

• nonn

Comments

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:
   5: {3}
   7: {4}
   9: {2,2}
  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}
  29: {10}
  31: {11}
  33: {2,5}
  34: {1,7}
  35: {3,4}
		

Crossrefs

Positions of negative terms in A325794.

Heinz numbers of the partitions counted by A325833.

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

Cf. A325694, A325780, A325781, A325792, A325793, A325795, A325796, A325798.

Programs

Mathematica

Select[Range[100],DivisorSigma[0,#]PrimePi[p]*k]]&]