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A088887
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Number of different prime signatures of the m values when A056239(m) is equal to n.
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9
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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
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OFFSET
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0,3
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COMMENTS
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Cardinality of set of multisets of multiplicities of parts of all partitions of n. - Vladeta Jovovic, May 25 2008
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LINKS
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EXAMPLE
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a(7) = 10: [1], [7], [1,1], [1,2], [1,3] [1,4], [1,5], [2,3], [1,1,1], [1,1,2].
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MAPLE
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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)):
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MATHEMATICA
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a[n_] := Sort /@ ((Length /@ Split[#])& /@ IntegerPartitions[n]) // Union // Length;
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PROG
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(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
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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