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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-François 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.)