A123557 -id:A123557

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A064688

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

+10
16

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

(list; graph; refs; listen; history; text; internal format)

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.

KEYWORD

nonn

AUTHOR

Jason Earls, Oct 11 2001

STATUS

approved

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