A324588 Heinz numbers of integer partitions of n into perfect squares (A001156).

1, 2, 4, 7, 8, 14, 16, 23, 28, 32, 46, 49, 53, 56, 64, 92, 97, 98, 106, 112, 128, 151, 161, 184, 194, 196, 212, 224, 227, 256, 302, 311, 322, 343, 368, 371, 388, 392, 419, 424, 448, 454, 512, 529, 541, 604, 622, 644, 661, 679, 686, 736, 742, 776, 784, 827, 838

Offset: 1

Author

Gus Wiseman, Mar 08 2019

Keywords

• nonn

Comments

The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).

Also products of elements of A011757.

Examples

			The sequence of terms together with their prime indices begins:
   1: {}
   2: {1}
   4: {1,1}
   7: {4}
   8: {1,1,1}
  14: {1,4}
  16: {1,1,1,1}
  23: {9}
  28: {1,1,4}
  32: {1,1,1,1,1}
  46: {1,9}
  49: {4,4}
  53: {16}
  56: {1,1,1,4}
  64: {1,1,1,1,1,1}
  92: {1,1,9}
  97: {25}
  98: {1,4,4}
		

Crossrefs

Cf. A001156, A011757, A033461, A052335, A056239, A062457, A078135, A112798, A117144, A118914, A276078.

Cf. A109298, A324524, A324525, A324571, A324572, A324587.

Programs

Mathematica

Select[Range[100],And@@Cases[FactorInteger[#],{p_,_}:>IntegerQ[Sqrt[PrimePi[p]]]]&]