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Number of different values of A000005(m) when A056239(m) is equal to n.
11

%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