%I #21 Jan 08 2016 06:15:53
%S 1,1,2,2,5,4,8,6,12,10,16,13,25,18,28,25,40,32,51,40,62,51,76,62,99,
%T 77,112,92,138,109,165,130,189,153,220,178,267,208,292,240,347,274,
%U 397,315,445,361,512,407,591,464,647,524,746,588,830,664,928,746,1034
%N Number of different values of A000005(m) when A056239(m) is equal to n.
%C Number of distinct values of Product_{k=1..n} (m(k,P)+1) where m(k,P) is multiplicity of part k in partition P, as P ranges over all partitions of n. - _Vladeta Jovovic_, May 24 2008
%H Alois P. Heinz, <a href="/A088880/b088880.txt">Table of n, a(n) for n = 0..222</a>
%p multipl := proc(P,p)
%p local a;
%p a := 0 ;
%p for el in P do
%p if el = p then
%p a := a+1 ;
%p end if;
%p end do;
%p a ;
%p end proc:
%p A088880 := proc(n)
%p local pro,pa,m,p;
%p pro := {} ;
%p for pa in combinat[partition](n) do
%p m := 1 ;
%p for p from 1 to n do
%p m := m*(1+multipl(pa,p)) ;
%p end do:
%p pro := pro union {m} ;
%p end do:
%p nops(pro) ;
%p end proc: # _R. J. Mathar_, Sep 27 2011
%p # second Maple program
%p b:= proc(n, i) option remember; `if`(n=0 or i<2, {n+1},
%p {seq(map(p->p*(j+1), b(n-i*j, i-1))[], j=0..n/i)})
%p end:
%p a:= n-> nops(b(n, n)):
%p seq(a(n), n=0..50); # _Alois P. Heinz_, Aug 09 2012
%t b[n_, i_] := b[n, i] = If[n==0 || i<2, {n+1}, Table[b[n-i*j, i-1]*(j+1), {j, 0, n/i}] // Flatten // Union]; a[n_] := Length[b[n, n]]; Table[a[n], {n, 0, 50}] (* _Jean-François Alcover_, Jan 08 2016, after _Alois P. Heinz_ *)
%Y Cf. A088314, A215366.
%K easy,nonn
%O 0,3
%A _Naohiro Nomoto_, Nov 28 2003