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A325129 Heinz numbers of integer partitions into nonsquares (A087153). 2
1, 3, 5, 9, 11, 13, 15, 17, 19, 25, 27, 29, 31, 33, 37, 39, 41, 43, 45, 47, 51, 55, 57, 59, 61, 65, 67, 71, 73, 75, 79, 81, 83, 85, 87, 89, 93, 95, 99, 101, 103, 107, 109, 111, 113, 117, 121, 123, 125, 127, 129, 131, 135, 137, 139, 141, 143, 145, 149, 153, 155 (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).

LINKS

Table of n, a(n) for n=1..61.

EXAMPLE

The sequence of terms together with their prime indices begins:

   1: {}

   3: {2}

   5: {3}

   9: {2,2}

  11: {5}

  13: {6}

  15: {2,3}

  17: {7}

  19: {8}

  25: {3,3}

  27: {2,2,2}

  29: {10}

  31: {11}

  33: {2,5}

  37: {12}

  39: {2,6}

  41: {13}

  43: {14}

  45: {2,2,3}

MATHEMATICA

Select[Range[100], !MemberQ[If[#==1, {}, FactorInteger[#]], {p_, _}/; IntegerQ[Sqrt[PrimePi[p]]]]&]

CROSSREFS

Cf. A001156, A011757, A033461, A056239, A062457, A066328, A087153, A112798.

Cf. A324571, A324587, A324588, A325128, A325130.

Sequence in context: A088607 A296243 A162699 * A173263 A285141 A329095

Adjacent sequences:  A325126 A325127 A325128 * A325130 A325131 A325132

KEYWORD

nonn

AUTHOR

Gus Wiseman, Apr 01 2019

STATUS

approved

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Last modified April 16 12:45 EDT 2021. Contains 343037 sequences. (Running on oeis4.)