A (probably wrong) conjecture

[Vladeta Jovovic]

>
> %I A000001
> %S A000001 
> 1,2,2,3,3,5,4,8,7,11,11,17,16,25,24,35,35,50,49,70,69,94,96,129,129,172,174,227,232,298,303,389,396,498,513,639,655,814,834,1025
> %N A000001 Number of distinct values of Product_{p is a part of P} (p-1) 
> when P ranges over all partitions of n.
> %F A000001 Conjecture:  G.f. is 
> x/(1-x)+((1-x^12)/((1-x^2)*(1-x^5)))*(1/Product_{k>0} (1-x^(prime(k)+1))), 
> i.e. a(n) = 1 + number of partitions of n into parts of the form p+1, p a 
> prime, excluding 12 and including 2 and 5.
> %Y A000001 Cf. A034891.
> %O A000001 1
> %K A000001 ,more,nonn,
> %A A000001 Vladeta Jovovic (vladeta at Eunet.yu), May 23 2008
>

V.