A324562 Numbers > 1 where the maximum prime index is greater than or equal to the number of prime factors counted with multiplicity.

2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15, 17, 19, 20, 21, 22, 23, 25, 26, 28, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 82, 83, 84, 85

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 enumerated by A064174. 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}
   3: {2}
   5: {3}
   6: {1,2}
   7: {4}
   9: {2,2}
  10: {1,3}
  11: {5}
  13: {6}
  14: {1,4}
  15: {2,3}
  17: {7}
  19: {8}
  20: {1,1,3}
  21: {2,4}
  22: {1,5}
  23: {9}
  25: {3,3}
  26: {1,6}
  28: {1,1,4}
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001222, A003114, A055396, A056239, A061395, A064174, A106529, A112798.

Cf. A324517, A324519, A324521, A324522, A324560, A324562.

Programs

Maple

with(numtheory):
q:= n-> is(pi(max(factorset(n)))>=bigomega(n)):
select(q, [$2..100])[];  # Alois P. Heinz, Mar 07 2019

Mathematica

Select[Range[2,100],PrimePi[FactorInteger[#][[-1,1]]]>=PrimeOmega[#]&]

Formula

A061395(a(n)) >= A001222(a(n)).