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A236937 Number of partitions of n such that the parts include all primes, with multiplicity, dividing n. 3
1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 1, 7, 1, 7, 15, 22, 1, 42, 1, 56, 56, 30, 1, 176, 176, 56, 385, 297, 1, 627, 1, 1002, 490, 176, 1255, 2436, 1, 297, 1255, 4565, 1, 5604, 1, 4565, 12310, 792, 1, 21637, 14883, 26015, 6842, 14883, 1, 63261, 31185, 63261, 14883 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,9

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000

EXAMPLE

With n = 9, 9 = 3 * 3.  Since 9 - (3 + 3) = 3, and the partitions of 3 are {(3), (2, 1) (1, 1, 1), the partitions of 9 that include (3, 3) are {(3, 3, 3), (3, 3, 2, 1), and (3, 3, 1, 1, 1), so a(9) = 3.

MAPLE

with(combinat):

a:= n-> numbpart(n-add(i[1]*i[2], i=ifactors(n)[2])):

seq(a(n), n=0..100);  # Alois P. Heinz, Feb 04 2014

MATHEMATICA

a[n_] := PartitionsP[n-Sum[i[[1]]*i[[2]], {i, FactorInteger[n]}]]; Table[ a[n], {n, 0, 100}] (* Jean-Fran├žois Alcover, Nov 11 2015, after Alois P. Heinz *)

CROSSREFS

Cf. A236938, A237125.

Sequence in context: A214734 A120653 A323850 * A323748 A116155 A144149

Adjacent sequences:  A236934 A236935 A236936 * A236938 A236939 A236940

KEYWORD

nonn

AUTHOR

J. Stauduhar, Feb 01 2014

EXTENSIONS

More terms from Alois P. Heinz, Feb 04 2014

STATUS

approved

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Last modified August 25 09:44 EDT 2019. Contains 326324 sequences. (Running on oeis4.)