A324561 Numbers with at least one prime index equal to 0, 1, or 4 modulo 5.

2, 4, 6, 7, 8, 10, 11, 12, 13, 14, 16, 18, 20, 21, 22, 23, 24, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 38, 39, 40, 42, 43, 44, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 58, 60, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77, 78, 80, 82, 84, 86, 87

Offset: 1

Author

Gus Wiseman, Mar 06 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.

Also Heinz numbers of the integer partitions counted by A039900. 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:
   2: {1}
   4: {1,1}
   6: {1,2}
   7: {4}
   8: {1,1,1}
  10: {1,3}
  11: {5}
  12: {1,1,2}
  13: {6}
  14: {1,4}
  16: {1,1,1,1}
  18: {1,2,2}
  20: {1,1,3}
  21: {2,4}
  22: {1,5}
  23: {9}
  24: {1,1,1,2}
		

Crossrefs

Cf. A008854, A039900, A055396, A056239, A061395, A106529, A112798.

Cf. A324519, A324521, A324522, A324560, A324561, A324562.

Programs

Maple

with(numtheory):
q:= n-> is(irem(pi(min(factorset(n))), 5) in {0, 1, 4}):
select(q, [$2..100])[];  # Alois P. Heinz, Mar 07 2019

Mathematica

Select[Range[100],Intersection[Mod[If[#==1,{},PrimePi/@First/@FactorInteger[#]],5],{0,1,4}]!={}&]