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 A088887 Number of different prime signatures of the m values when A056239(m) is equal to n. 9
 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 (list; graph; refs; listen; history; text; internal format)
 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 * A265546 A066911 A326229 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

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Last modified October 4 12:40 EDT 2023. Contains 365877 sequences. (Running on oeis4.)