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

1,1

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).

Links

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

Example

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}

Mathematica

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

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.

Sequence in context: A279289 A175382 A279244 * A128163 A177088 A362486

Adjacent sequences: A325794 A325795 A325796 * A325798 A325799 A325800

Keyword

nonn

Author

Gus Wiseman, May 23 2019

Status

approved