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 A266499 Number of partitions of n with product of multiplicities of parts equal to n. 2
 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 8, 1, 5, 1, 11, 6, 5, 1, 48, 7, 9, 21, 39, 1, 104, 1, 143, 27, 20, 45, 457, 1, 32, 58, 620, 1, 549, 1, 363, 514, 65, 1, 4302, 118, 858, 207, 926, 1, 4080, 437, 5171, 382, 181, 1, 20398, 1, 251, 4287, 20582, 1212 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 FORMULA a(n) = A266477(n,n). p in primes => a(p) = 1. EXAMPLE a(8) = 2 because among the 22 (= A000041(8)) partitions of 8 only [1,1,1,1,1,1,1,1] and [1,1,1,1,2,2] have product of multiplicities of parts equal to 8. MAPLE b:= proc(n, i, p) option remember; `if`(p=1 and i*(i+1)/2 `if`(isprime(n), 1, b(n\$3)): seq(a(n), n=0..70); MATHEMATICA b[n_, i_, p_] := b[n, i, p] = If[p == 1 && i*(i + 1)/2 < n, 0, If[n == 0, If[p == 1, 1, 0], If[i < 1, 0, b[n, i - 1, p] + Sum[If[Mod[p, j] == 0, b[n - i*j, i - 1, p/j], 0], {j, 1, Min[p, n/i]}]]]]; a[n_] := If[PrimeQ[n], 1, b[n, n, n]]; Table[a[n], {n, 0, 70}] (* Jean-François Alcover, Dec 22 2016, after Alois P. Heinz *) CROSSREFS Main diagonal of A266477. Cf. A000040, A000041. Sequence in context: A124767 A319443 A130633 * A226621 A112933 A270650 Adjacent sequences:  A266496 A266497 A266498 * A266500 A266501 A266502 KEYWORD nonn AUTHOR Emeric Deutsch and Alois P. Heinz, Dec 30 2015 STATUS approved

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Last modified April 10 15:07 EDT 2021. Contains 342845 sequences. (Running on oeis4.)