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

1,1

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 enumerated by A064174. The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).

Links

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

Formula

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

Example

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}

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[#]&]

Crossrefs

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

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

Sequence in context: A092418 A004195 A354514 * A352489 A370422 A371170

Adjacent sequences: A324559 A324560 A324561 * A324563 A324564 A324565

Keyword

nonn

Author

Gus Wiseman, Mar 06 2019

Status

approved