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 A320638 Triangle T(n,k) read by rows: the number of partitions of n into k parts which are divisors of n. 1
 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 2, 2, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 3, 7, 8, 8, 6, 4, 3, 2, 1, 1, 1, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,18 LINKS FORMULA T(n,n) = T(n,1) =1; representing partitions into the trivial divisors. EXAMPLE The triangle starts 1 1 1 1 0 1 1 1 1 1 1 0 0 0 1 1 1 2 2 1 1 1 0 0 0 0 0 1 1 1 1 2 2 1 1 1 1 0 1 0 1 0 1 0 1 1 1 0 1 2 2 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 3 7 8 8 6 4 3 2 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 2 2 1 1 1 1 1 1 1 0 1 0 3 0 3 0 2 0 2 0 1 0 1 1 1 1 2 3 4 4 4 4 3 2 2 2 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 2 3 6 8 9 10 9 8 6 5 4 3 2 2 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 3 6 8 10 10 9 9 8 6 5 4 3 3 2 1 1 1 1 0 1 0 1 0 3 0 3 0 2 0 2 0 2 0 1 0 1 0 1 1 1 0 0 0 0 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 3 9 20 33 44 50 51 48 42 36 29 23 18 14 11 8 6 4 3 2 1 1 MAPLE A320638 := proc(n, noprts) local a, p, w, el ; a := 0 ; for p in combinat[partition](n) do if nops(p) = noprts then w := true ; for el in p do if modp(n, el) <> 0 then w := false; break; end if; end do: if w then a := a+1 ; end if; end if ; end do: a ; end proc: seq(seq(A320638(n, k), k=1..n), n=1..13) ; CROSSREFS Cf. A018818 (row sums), A008284. Sequence in context: A004562 A261817 A123550 * A262045 A263087 A204433 Adjacent sequences: A320635 A320636 A320637 * A320639 A320640 A320641 KEYWORD nonn,tabl AUTHOR R. J. Mathar, Oct 18 2018 STATUS approved

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Last modified March 24 13:51 EDT 2023. Contains 361479 sequences. (Running on oeis4.)