A324517 Numbers > 1 where the maximum prime index equals the number of prime factors minus the number of distinct prime factors.

4, 24, 27, 36, 54, 80, 200, 224, 240, 360, 405, 500, 540, 600, 625, 672, 675, 704, 784, 810, 900, 1008, 1120, 1125, 1250, 1350, 1500, 1512, 1664, 1701, 1875, 2112, 2250, 2268, 2352, 2744, 2800, 3168, 3360, 3402, 3520, 3528, 3750, 3872, 3920, 3969, 4352, 4752

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 A324518. 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}
   24: {1,1,1,2}
   27: {2,2,2}
   36: {1,1,2,2}
   54: {1,2,2,2}
   80: {1,1,1,1,3}
  200: {1,1,1,3,3}
  224: {1,1,1,1,1,4}
  240: {1,1,1,1,2,3}
  360: {1,1,1,2,2,3}
  405: {2,2,2,2,3}
  500: {1,1,3,3,3}
  540: {1,1,2,2,2,3}
  600: {1,1,1,2,3,3}
  625: {3,3,3,3}
  672: {1,1,1,1,1,2,4}
  675: {2,2,2,3,3}
  704: {1,1,1,1,1,1,5}
  784: {1,1,1,1,4,4}
  810: {1,2,2,2,2,3}
  900: {1,1,2,2,3,3}
		

Crossrefs

Cf. A001221, A001222, A046660, A056239, A061395, A112798, A243055, A256617.

Cf. A324515, A324518, A324519, A324521, A324522, A324560, A324562.

Programs

Mathematica

Select[Range[2,1000],With[{f=FactorInteger[#]},PrimePi[f[[-1,1]]]==Total[Last/@f]-Length[f]]&]

Formula

A061395(a(n)) = A001222(a(n)) - A001221(a(n)) = A046660(a(n)).