A324560 Numbers > 1 where the minimum prime index is less than or equal to the number of prime factors counted with multiplicity.

2, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 33, 34, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 56, 57, 58, 60, 62, 63, 64, 66, 68, 69, 70, 72, 74, 75, 76, 78, 80, 81, 82, 84, 86, 87, 88, 90, 92, 93, 94, 96, 98, 99, 100

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 a certain type of integer partitions counted by A039900 (but not the type of partitions described in the name). 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.

Formula

A055396(a(n)) <= A001222(a(n)).

Example

The sequence of terms together with their prime indices begins:
   2: {1}
   4: {1,1}
   6: {1,2}
   8: {1,1,1}
   9: {2,2}
  10: {1,3}
  12: {1,1,2}
  14: {1,4}
  15: {2,3}
  16: {1,1,1,1}
  18: {1,2,2}
  20: {1,1,3}
  21: {2,4}
  22: {1,5}
  24: {1,1,1,2}
  26: {1,6}
  27: {2,2,2}
  28: {1,1,4}
  30: {1,2,3}
  32: {1,1,1,1,1}

Maple

with(numtheory):
q:= n-> is(pi(min(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, A039900, A055396, A056239, A061395, A106529, A112798.

Cf. A324515, A324517, A324519, A324521, A324522, A324560, A324562.

Sequence in context: A338924 A065090 A371167 * A355822 A367226 A227197

Adjacent sequences: A324557 A324558 A324559 * A324561 A324562 A324563

Keyword

nonn

Author

Gus Wiseman, Mar 06 2019

Status

approved