A324522 Numbers > 1 where the minimum prime index is equal to the number of prime factors counted with multiplicity.

2, 9, 15, 21, 33, 39, 51, 57, 69, 87, 93, 111, 123, 125, 129, 141, 159, 175, 177, 183, 201, 213, 219, 237, 245, 249, 267, 275, 291, 303, 309, 321, 325, 327, 339, 381, 385, 393, 411, 417, 425, 447, 453, 455, 471, 475, 489, 501, 519, 537, 543, 573, 575, 579, 591

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 integer partitions where the minimum part is equal to the number of parts (A006141). 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}
    9: {2,2}
   15: {2,3}
   21: {2,4}
   33: {2,5}
   39: {2,6}
   51: {2,7}
   57: {2,8}
   69: {2,9}
   87: {2,10}
   93: {2,11}
  111: {2,12}
  123: {2,13}
  125: {3,3,3}
  129: {2,14}
  141: {2,15}
  159: {2,16}
  175: {3,3,4}
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001222, A006141, A055396, A056239, A106529, A112798, A256617.

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

Programs

Maple

with(numtheory):
q:= n-> is(pi(min(factorset(n)))=bigomega(n)):
select(q, [$2..600])[];  # Alois P. Heinz, Mar 07 2019

Mathematica

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

Formula

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