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

1,2

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.

Links

Table of n, a(n) for n=1..57.

Example

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}

Mathematica

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

Crossrefs

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

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

Sequence in context: A327478 A062846 A102824 * A201364 A225318 A308267

Adjacent sequences: A324585 A324586 A324587 * A324589 A324590 A324591

Keyword

nonn

Author

Gus Wiseman, Mar 08 2019

Status

approved