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A324588 Heinz numbers of integer partitions of n into perfect squares (A001156). 9
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 7 20:36 EDT 2021. Contains 343652 sequences. (Running on oeis4.)