A325694 Numbers with one fewer divisors than the sum of their prime indices.

5, 9, 14, 15, 44, 45, 50, 78, 104, 105, 110, 135, 196, 225, 272, 276, 342, 380, 405, 476, 572, 585, 608, 650, 693, 726, 735, 825, 888, 930, 968, 1125, 1215, 1218, 1240, 1472, 1476, 1482, 1518, 1566, 1610, 1624, 1976, 1995, 2024, 2090, 2210, 2256, 2565, 2618

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).

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are Heinz numbers of the partitions counted by A325836.

Examples

			The sequence of terms together with their prime indices begins:
     5: {3}
     9: {2,2}
    14: {1,4}
    15: {2,3}
    44: {1,1,5}
    45: {2,2,3}
    50: {1,3,3}
    78: {1,2,6}
   104: {1,1,1,6}
   105: {2,3,4}
   110: {1,3,5}
   135: {2,2,2,3}
   196: {1,1,4,4}
   225: {2,2,3,3}
   272: {1,1,1,1,7}
   276: {1,1,2,9}
   342: {1,2,2,8}
   380: {1,1,3,8}
   405: {2,2,2,2,3}
   476: {1,1,4,7}
		

Crossrefs

Positions of -1's in A325794.

Cf. A000005, A056239, A112798, A325780, A325792, A325793, A325794, A325795, A325796, A325797, A325798, A325836.

Programs

Mathematica

Select[Range[1000],DivisorSigma[0,#]==Total[Cases[FactorInteger[#],{p_,k_}:>PrimePi[p]*k]]-1&]