A324929 Numbers whose product of prime indices is even.

3, 6, 7, 9, 12, 13, 14, 15, 18, 19, 21, 24, 26, 27, 28, 29, 30, 33, 35, 36, 37, 38, 39, 42, 43, 45, 48, 49, 51, 52, 53, 54, 56, 57, 58, 60, 61, 63, 65, 66, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 81, 84, 86, 87, 89, 90, 91, 93, 95, 96, 98, 99, 101, 102, 104

Offset: 1

Author

Gus Wiseman, Mar 21 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 product A003963(n).

Also Heinz numbers of integer partitions whose product of parts is even (counted by A047967), where the Heinz number of an integer partition (y_1,...,y_k) is prime(y_1) * ... * prime(y_k).

Examples

			The sequence of terms together with their prime indices begins:
   3: {2}
   6: {1,2}
   7: {4}
   9: {2,2}
  12: {1,1,2}
  13: {6}
  14: {1,4}
  15: {2,3}
  18: {1,2,2}
  19: {8}
  21: {2,4}
  24: {1,1,1,2}
  26: {1,6}
  27: {2,2,2}
  28: {1,1,4}
  29: {10}
  30: {1,2,3}
  33: {2,5}
  35: {3,4}
  36: {1,1,2,2}
		

Crossrefs

Cf. A000720, A001222, A003963, A005087, A033844, A047967, A066208, A112798, A257992, A318400, A324927.

Programs

Mathematica

Select[Range[100],EvenQ[Times@@PrimePi/@If[#==1,{},FactorInteger[#]][[All,1]]]&]

PARI

isok(n) = my(f=factor(n)[,1]); !(prod(k=1, #f, primepi(f[k])) % 2); \\ Michel Marcus, Mar 22 2019