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 A055923 Number of partitions of n in which each part occurs a prime number (or 0) times. 16
 1, 0, 1, 1, 1, 1, 3, 2, 3, 4, 4, 6, 8, 8, 10, 13, 13, 20, 20, 24, 26, 38, 35, 51, 51, 65, 67, 92, 86, 121, 117, 153, 155, 209, 197, 270, 262, 339, 341, 444, 425, 565, 555, 703, 711, 903, 884, 1135, 1128, 1397, 1430, 1766, 1757, 2193, 2214, 2691, 2762, 3344 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Alois P. Heinz) FORMULA EULER transform of b where b has g.f. Sum {k>0} c(k)*x^k/(1-x^k) where c is inverse EULER transform of characteristic function of prime numbers. G.f.: Product(1+Sum(x^(i*prime(k)), k=1..infinity), i=1..infinity). - Vladeta Jovovic, Jan 08 2005 MAPLE b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(`if`(isprime(j), b(n-i*j, i-1), 0), j=1..n/i) +b(n, i-1))) end: a:= n-> b(n\$2): seq(a(n), n=0..60); # Alois P. Heinz, May 31 2014 MATHEMATICA b[n_, i_] := b[n, i] = If[n == 0, 1, If[i<1, 0, Sum[If[PrimeQ[j], b[n-i*j, i-1], 0], {j, 1, n/i}] + b[n, i-1]]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Nov 11 2015, after Alois P. Heinz *) CROSSREFS Cf. A000041, A007690, A055922. Sequence in context: A075988 A029150 A255246 * A035634 A091563 A161985 Adjacent sequences: A055920 A055921 A055922 * A055924 A055925 A055926 KEYWORD nonn AUTHOR Christian G. Bower, Jun 23 2000 STATUS approved

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Last modified December 8 01:51 EST 2022. Contains 358672 sequences. (Running on oeis4.)