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

1,1

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 A324520. 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

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

Example

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}

Mathematica

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

Crossrefs

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

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

Sequence in context: A362873 A111371 A078514 * A230628 A074285 A301252

Adjacent sequences: A324516 A324517 A324518 * A324520 A324521 A324522

Keyword

nonn

Author

Gus Wiseman, Mar 06 2019

Status

approved