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A088880 Number of different values of A000005(m) when A056239(m) is equal to n.

%I A088880 #21 Jan 08 2016 06:15:53
%S A088880 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 A088880 77,112,92,138,109,165,130,189,153,220,178,267,208,292,240,347,274,
%U A088880 397,315,445,361,512,407,591,464,647,524,746,588,830,664,928,746,1034
%N A088880 Number of different values of A000005(m) when A056239(m) is equal to n.
%C A088880 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 A088880 Alois P. Heinz, <a href="/A088880/b088880.txt">Table of n, a(n) for n = 0..222</a>
%p A088880 multipl := proc(P,p)
%p A088880         local a;
%p A088880         a := 0 ;
%p A088880         for el in P do
%p A088880                 if el = p then
%p A088880                         a := a+1 ;
%p A088880                 end if;
%p A088880         end do;
%p A088880         a ;
%p A088880 end proc:
%p A088880 A088880 := proc(n)
%p A088880         local pro,pa,m,p;
%p A088880         pro := {} ;
%p A088880         for pa in combinat[partition](n) do
%p A088880                 m := 1 ;
%p A088880                 for p from 1 to n do
%p A088880                         m := m*(1+multipl(pa,p)) ;
%p A088880                 end do:
%p A088880                 pro := pro union {m} ;
%p A088880         end do:
%p A088880         nops(pro) ;
%p A088880 end proc: # _R. J. Mathar_, Sep 27 2011
%p A088880 # second Maple program
%p A088880 b:= proc(n, i) option remember; `if`(n=0 or i<2, {n+1},
%p A088880        {seq(map(p->p*(j+1), b(n-i*j, i-1))[], j=0..n/i)})
%p A088880     end:
%p A088880 a:= n-> nops(b(n, n)):
%p A088880 seq(a(n), n=0..50);  # _Alois P. Heinz_, Aug 09 2012
%t A088880 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 A088880 Cf. A088314, A215366.
%K A088880 easy,nonn
%O A088880 0,3
%A A088880 _Naohiro Nomoto_, Nov 28 2003