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A239509 Number of partitions of n into distinct nonprime squarefree numbers, cf. A000469.

%I A239509 #11 Jan 15 2016 10:27:39
%S A239509 1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,2,2,1,0,0,1,3,3,1,1,2,2,2,2,2,3,4,4,3,
%T A239509 2,4,7,6,4,5,6,6,7,7,6,8,10,9,9,10,10,12,13,12,13,15,16,18,18,16,17,
%U A239509 21,23,23,23,25,28,29,29,31,34,37,41,40,38,42,46
%N A239509 Number of partitions of n into distinct nonprime squarefree numbers, cf. A000469.
%H A239509 Alois P. Heinz, <a href="/A239509/b239509.txt">Table of n, a(n) for n = 0..10000</a>
%e A239509 a(30) = #{30, 15+14+1, 14+10+6} = 3;
%e A239509 a(31) = #{30+1, 21+10, 15+10+6, 14+10+6+1} = 4;
%e A239509 a(32) = #{26+6, 22+10, 21+10+1, 15+10+6+1} = 4;
%e A239509 a(33) = #{33, 26+6+1, 22+10+1} = 3;
%e A239509 a(34) = #{34, 33+1} = 2;
%e A239509 a(35) = #{35, 34+1, 21+14, 15+14+6} = 4;
%e A239509 a(36) = #{35+1, 30+6, 26+10, 22+14, 21+15, 21+14+1, 15+14+6+1} = 7.
%p A239509 b:= proc(n, i) option remember; `if`(i*(i+1)/2<n, 0,
%p A239509       `if`(n=0, 1, b(n, i-1) +`if`(i<=n and not
%p A239509       isprime(i) and issqrfree(i), b(n-i, i-1), 0)))
%p A239509     end:
%p A239509 a:= n-> b(n$2):
%p A239509 seq(a(n), n=0..100);  # _Alois P. Heinz_, Jun 02 2015
%t A239509 b[n_, i_] := b[n, i] = If[i*(i+1)/2<n, 0, If[n==0, 1, b[n, i-1] + If[i <= n && !PrimeQ[i] && SquareFreeQ[i], b[n-i, i-1], 0]]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Jan 15 2016, after _Alois P. Heinz_ *)
%o A239509 (Haskell)
%o A239509 a239509 = p a000469_list where
%o A239509    p _      0 = 1
%o A239509    p (k:ks) m = if m < k then 0 else p ks (m - k) + p ks m
%Y A239509 Cf. A239508, A087188.
%K A239509 nonn
%O A239509 0,16
%A A239509 _Reinhard Zumkeller_, Mar 21 2014