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

0,3

Comments

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

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A088314.

Sequence in context: A325412 A265562 A140312 * A368085 A265546 A066911

Adjacent sequences: A088884 A088885 A088886 * A088888 A088889 A088890

Keyword

easy,nonn

Author

Naohiro Nomoto, Nov 28 2003

Extensions

More terms from Vladeta Jovovic, May 25 2008

Status

approved