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A324587 Heinz numbers of integer partitions of n into distinct perfect squares (A033461). 8
1, 2, 7, 14, 23, 46, 53, 97, 106, 151, 161, 194, 227, 302, 311, 322, 371, 419, 454, 541, 622, 661, 679, 742, 827, 838, 1009, 1057, 1082, 1193, 1219, 1322, 1358, 1427, 1589, 1619, 1654, 1879, 2018, 2114, 2143, 2177, 2231, 2386, 2437, 2438, 2741, 2854, 2933 (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 distinct elements of A011757.

LINKS

Table of n, a(n) for n=1..49.

EXAMPLE

The sequence of terms together with their prime indices begins:

    1: {}

    2: {1}

    7: {4}

   14: {1,4}

   23: {9}

   46: {1,9}

   53: {16}

   97: {25}

  106: {1,16}

  151: {36}

  161: {4,9}

  194: {1,25}

  227: {49}

  302: {1,36}

  311: {64}

  322: {1,4,9}

  371: {4,16}

  419: {81}

  454: {1,49}

  541: {100}

MATHEMATICA

Select[Range[1000], And@@Cases[FactorInteger[#], {p_, k_}:>k==1&&IntegerQ[Sqrt[PrimePi[p]]]]&]

CROSSREFS

Cf. A001156, A005117, A011757, A033461, A052335, A056239, A062457, A078135, A112798, A117144, A276078.

Cf. A109298, A324524, A324525, A324571, A324572, A324588.

Sequence in context: A008865 A227582 A249852 * A018392 A051640 A119354

Adjacent sequences:  A324584 A324585 A324586 * A324588 A324589 A324590

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.)