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A055923 Number of partitions of n in which each part occurs a prime number (or 0) times. 3
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

Alois P. Heinz, Table of n, a(n) for n = 0..1000

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-Fran├žois 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 January 22 05:11 EST 2019. Contains 319353 sequences. (Running on oeis4.)