A038499 Number of partitions of n into a prime number of parts.

1, 0, 1, 2, 3, 5, 7, 10, 13, 18, 23, 31, 39, 52, 65, 84, 104, 134, 165, 210, 258, 324, 397, 495, 603, 747, 908, 1115, 1351, 1652, 1993, 2425, 2918, 3531, 4237, 5106, 6105, 7330, 8741, 10449, 12425, 14804, 17549, 20839, 24637, 29155, 34377, 40559, 47688, 56100

Offset

0,4

Comments

Also, number of partitions of n whose largest part is a prime. E.g., for a(7) = 10 we have 6+1 = 5+2 = 4+3 = 5+1+1 = 4+2+1 = 3+3+1 = 3+2+2 = 3+1+1+1+1 = 2+2+1+1+1 = 1+1+1+1+1+1+1 and 7 = 5+2 = 5+1+1 = 3+3+1 = 3+2+2 = 3+2+1+1 = 3+1+1+1+1 = 2+2+2+1 = 2+2+1+1+1 = 2+1+1+1+1+1. - Jon Perry Jul 06 2004

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Formula

G.f.: Sum_{n>=1}(x^prime(n)/Product_{i=1..prime(n)}(1-x^i)). - Vladeta Jovovic, Dec 25 2003

Maple

with(numtheory):
b:= proc(n, i) option remember; `if`(n<0, 0,
      `if`(n=0 or i=1, 1, `if`(i<1, 0, b(n, i-1)+
      `if`(i>n, 0, b(n-i, i)))))
    end:
a:= n-> `if`(n=0, 1, add((p-> b(n-p, p)
           )(ithprime(i)), i=1..pi(n))):
seq(a(n), n=0..60);  # Alois P. Heinz, Sep 24 2015

Mathematica

nn=50; Table[CoefficientList[Series[x^p Product[1/(1-x^i), {i, 1, p}], {x, 0, nn}], x], {p, Table[Prime[m], {m, 1, PrimePi[nn]}]}]//Total  (* Geoffrey Critzer, Mar 10 2013 *)

Crossrefs

Cf. A027187, A027193.

Sequence in context: A347549 A008628 A363067 * A118199 A239883 A332283

Adjacent sequences: A038496 A038497 A038498 * A038500 A038501 A038502

Keyword

nonn

Author

Christian G. Bower, Feb 15 1999

Status

approved