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a(n) = number of partitions of primes into distinct (also odd) parts.
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%I #23 Dec 15 2017 17:35:42

%S 1,2,3,5,12,18,38,54,104,256,340,760,1260,1610,2590,5120,9792,12076,

%T 22250,32992,40026,70488,101698,173682,345856,483330,570078,789640,

%U 927406,1274118,3725410,5010688,7755776,8953856,18108418,20792120

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

%H Harry J. Smith, <a href="/A064688/b064688.txt">Table of n, a(n) for n=1..400</a>

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

%F a(n) = A000009(A000040(n)). - _Reinhard Zumkeller_, Dec 27 2002

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

%t a[n_]:=PartitionsQ[Prime[n]]; (* _Vladimir Joseph Stephan Orlovsky_, Dec 05 2008 *)

%o (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)),","))

%o (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

%Y Cf. A000009, A000040, A123557.

%K nonn

%O 1,2

%A _Jason Earls_, Oct 11 2001