A088887 Number of different prime signatures of the m values when A056239(m) is equal to n.

1, 1, 2, 3, 5, 5, 10, 10, 16, 18, 24, 27, 41, 42, 54, 63, 82, 88, 114, 123, 153, 169, 205, 224, 279, 296, 356, 389, 463, 499, 592, 638, 750, 803, 939, 996, 1173, 1253, 1441, 1543, 1772, 1891, 2158, 2305, 2619, 2780, 3166, 3358, 3805, 4026, 4522, 4810, 5405

Offset: 0

Author

Naohiro Nomoto, Nov 28 2003

Keywords

• easy
• nonn

Comments

Cardinality of set of multisets of multiplicities of parts of all partitions of n. - Vladeta Jovovic, May 25 2008

Examples

			a(7) = 10: [1], [7], [1,1], [1,2], [1,3] [1,4], [1,5], [2,3], [1,1,1], [1,1,2].
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..125

Crossrefs

Cf. A088314.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, {[]}, `if`(i<1, {},
      {b(n, i-1)[], seq(map(x->sort([x[], j]),
                    b(n-i*j, i-1))[], j=1..n/i)}))
    end:
a:= n-> nops(b(n, n)):
seq(a(n), n=0..50);  # Alois P. Heinz, Feb 19 2013

Mathematica

a[n_] := Sort /@ ((Length /@ Split[#])& /@ IntegerPartitions[n]) // Union // Length;
a /@ Range[0, 50] (* Jean-François Alcover, Oct 31 2020 *)

Python

from sympy.utilities.iterables import partitions
def A088887(n): return len({tuple(sorted(p.values())) for p in partitions(n)}) # Chai Wah Wu, Sep 10 2023

Extensions

More terms from Vladeta Jovovic, May 25 2008