A064688 a(n) = number of partitions of primes into distinct (also odd) parts.

1, 2, 3, 5, 12, 18, 38, 54, 104, 256, 340, 760, 1260, 1610, 2590, 5120, 9792, 12076, 22250, 32992, 40026, 70488, 101698, 173682, 345856, 483330, 570078, 789640, 927406, 1274118, 3725410, 5010688, 7755776, 8953856, 18108418, 20792120

Offset

1,2

Links

Harry J. Smith, Table of n, a(n) for n=1..400

Formula

a(n) = t(prime(n), 0), t as defined in A079211.

a(n) = A000009(A000040(n)). - Reinhard Zumkeller, Dec 27 2002

Maple

A := mul(1+x^m, m=1..100); A000009 := n->coeff(A, x, n); A064688:=n->A000009(ithprime(n));

Mathematica

a[n_]:=PartitionsQ[Prime[n]]; (* Vladimir Joseph Stephan Orlovsky, Dec 05 2008 *)

Prog

(PARI) q(n) = polcoeff(prod(k=1, n, 1+x^k, 1+x*O(x^n)), n) for(n=1, 50, print1(q(prime(n)), ", "))
(PARI) q(n)= { polcoeff(prod(k=1, n, 1 + x^k, 1 + x*O(x^n)), n) } { for (n = 1, 400, write("b064688.txt", n, " ", q(prime(n))) ) } \\ Harry J. Smith, Sep 22 2009

Crossrefs

Cf. A000009, A000040, A123557.

Sequence in context: A331101 A193776 A051915 * A089891 A282237 A004689

Adjacent sequences: A064685 A064686 A064687 * A064689 A064690 A064691

Keyword

nonn

Author

Jason Earls, Oct 11 2001

Status

approved