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

%I A088887 #24 Sep 10 2023 21:55:33
%S A088887 1,1,2,3,5,5,10,10,16,18,24,27,41,42,54,63,82,88,114,123,153,169,205,
%T A088887 224,279,296,356,389,463,499,592,638,750,803,939,996,1173,1253,1441,
%U A088887 1543,1772,1891,2158,2305,2619,2780,3166,3358,3805,4026,4522,4810,5405
%N A088887 Number of different prime signatures of the m values when A056239(m) is equal to n.
%C A088887 Cardinality of set of multisets of multiplicities of parts of all partitions of n. - _Vladeta Jovovic_, May 25 2008
%H A088887 Alois P. Heinz, <a href="/A088887/b088887.txt">Table of n, a(n) for n = 0..125</a>
%e A088887 a(7) = 10: [1], [7], [1,1], [1,2], [1,3] [1,4], [1,5], [2,3], [1,1,1], [1,1,2].
%p A088887 b:= proc(n, i) option remember; `if`(n=0, {[]}, `if`(i<1, {},
%p A088887       {b(n, i-1)[], seq(map(x->sort([x[], j]),
%p A088887                     b(n-i*j, i-1))[], j=1..n/i)}))
%p A088887     end:
%p A088887 a:= n-> nops(b(n, n)):
%p A088887 seq(a(n), n=0..50);  # _Alois P. Heinz_, Feb 19 2013
%t A088887 a[n_] := Sort /@ ((Length /@ Split[#])& /@ IntegerPartitions[n]) // Union // Length;
%t A088887 a /@ Range[0, 50] (* _Jean-François Alcover_, Oct 31 2020 *)
%o A088887 (Python)
%o A088887 from sympy.utilities.iterables import partitions
%o A088887 def A088887(n): return len({tuple(sorted(p.values())) for p in partitions(n)}) # _Chai Wah Wu_, Sep 10 2023
%Y A088887 Cf. A088314.
%K A088887 easy,nonn
%O A088887 0,3
%A A088887 _Naohiro Nomoto_, Nov 28 2003
%E A088887 More terms from _Vladeta Jovovic_, May 25 2008