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

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, 77, 112, 92, 138, 109, 165, 130, 189, 153, 220, 178, 267, 208, 292, 240, 347, 274, 397, 315, 445, 361, 512, 407, 591, 464, 647, 524, 746, 588, 830, 664, 928, 746, 1034

Offset: 0

Author

Naohiro Nomoto, Nov 28 2003

Keywords

• easy
• nonn

Comments

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..222

Crossrefs

Cf. A088314, A215366.

Programs

Maple

multipl := proc(P,p)
        local a;
        a := 0 ;
        for el in P do
                if el = p then
                        a := a+1 ;
                end if;
        end do;
        a ;
end proc:
A088880 := proc(n)
        local pro,pa,m,p;
        pro := {} ;
        for pa in combinat[partition](n) do
                m := 1 ;
                for p from 1 to n do
                        m := m*(1+multipl(pa,p)) ;
                end do:
                pro := pro union {m} ;
        end do:
        nops(pro) ;
end proc: # R. J. Mathar, Sep 27 2011
# second Maple program
b:= proc(n, i) option remember; `if`(n=0 or i<2, {n+1},
       {seq(map(p->p*(j+1), b(n-i*j, i-1))[], j=0..n/i)})
    end:
a:= n-> nops(b(n, n)):
seq(a(n), n=0..50);  # Alois P. Heinz, Aug 09 2012

Mathematica

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 *)