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

1,1

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.

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).

Links

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

Example

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}

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}]!={}&]

Crossrefs

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

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

Sequence in context: A014530 A268445 A053663 * A288258 A075313 A183858

Adjacent sequences: A324558 A324559 A324560 * A324562 A324563 A324564

Keyword

nonn

Author

Gus Wiseman, Mar 06 2019

Status

approved