A324519 Numbers > 1 where the minimum prime index equals the number of prime factors minus the number of distinct prime factors.

4, 12, 18, 20, 27, 28, 44, 50, 52, 60, 68, 76, 84, 90, 92, 98, 116, 124, 126, 132, 135, 140, 148, 150, 156, 164, 172, 188, 189, 198, 204, 212, 220, 225, 228, 234, 236, 242, 244, 260, 268, 276, 284, 292, 294, 297, 306, 308, 316, 332, 338, 340, 342, 348, 350

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 A324520. 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:
   4: {1,1}
  12: {1,1,2}
  18: {1,2,2}
  20: {1,1,3}
  27: {2,2,2}
  28: {1,1,4}
  44: {1,1,5}
  50: {1,3,3}
  52: {1,1,6}
  60: {1,1,2,3}
  68: {1,1,7}
  76: {1,1,8}
  84: {1,1,2,4}
  90: {1,2,2,3}
  92: {1,1,9}
  98: {1,4,4}
		

Links

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

Crossrefs

Cf. A001221, A001222, A046660, A055396, A056239, A061395, A106529, A112798.

Cf. A324515, A324517, A324520, A324521, A324522, A324560, A324562.

Programs

Mathematica

Select[Range[2,100],With[{f=FactorInteger[#]},PrimePi[f[[1,1]]]==Total[Last/@f]-Length[f]]&]

Formula

A055396(a(n)) = A001222(a(n)) - A001221(a(n)) = A046660(a(n)).