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A325363 Heinz numbers of integer partitions into nonzero triangular numbers A000217. 1
1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 29, 32, 40, 47, 50, 52, 58, 64, 65, 73, 80, 94, 100, 104, 107, 116, 125, 128, 130, 145, 146, 151, 160, 169, 188, 197, 200, 208, 214, 232, 235, 250, 256, 257, 260, 290, 292, 302, 317, 320, 325, 338, 365, 376, 377, 394, 397 (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).

The enumeration of these partitions by sum is given by A007294.

LINKS

Table of n, a(n) for n=1..58.

EXAMPLE

The sequence of terms together with their prime indices begins:

    1: {}

    2: {1}

    4: {1,1}

    5: {3}

    8: {1,1,1}

   10: {1,3}

   13: {6}

   16: {1,1,1,1}

   20: {1,1,3}

   25: {3,3}

   26: {1,6}

   29: {10}

   32: {1,1,1,1,1}

   40: {1,1,1,3}

   47: {15}

   50: {1,3,3}

   52: {1,1,6}

   58: {1,10}

   64: {1,1,1,1,1,1}

   65: {3,6}

MATHEMATICA

nn=1000;

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];

trgs=Table[n*(n+1)/2, {n, Sqrt[2*PrimePi[nn]]}];

Select[Range[nn], SubsetQ[trgs, primeMS[#]]&]

CROSSREFS

Cf. A000217, A007294, A056239, A112798, A240026, A325327, A325360, A325362, A325367, A325390, A325394, A325400.

Sequence in context: A144876 A239517 A231056 * A000549 A191985 A126026

Adjacent sequences:  A325360 A325361 A325362 * A325364 A325365 A325366

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 02 2019

STATUS

approved

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Last modified December 13 06:26 EST 2019. Contains 329968 sequences. (Running on oeis4.)