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

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, 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, 21, 23, 23, 23, 25, 28, 29, 29, 31, 34, 37, 41, 40, 38, 42, 46

Offset: 0

Author

Reinhard Zumkeller, Mar 21 2014

Keywords

• nonn

Examples

			a(30) = #{30, 15+14+1, 14+10+6} = 3;
a(31) = #{30+1, 21+10, 15+10+6, 14+10+6+1} = 4;
a(32) = #{26+6, 22+10, 21+10+1, 15+10+6+1} = 4;
a(33) = #{33, 26+6+1, 22+10+1} = 3;
a(34) = #{34, 33+1} = 2;
a(35) = #{35, 34+1, 21+14, 15+14+6} = 4;
a(36) = #{35+1, 30+6, 26+10, 22+14, 21+15, 21+14+1, 15+14+6+1} = 7.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A239508, A087188.

Programs

Haskell

a239509 = p a000469_list where
   p _      0 = 1
   p (k:ks) m = if m < k then 0 else p ks (m - k) + p ks m

Maple

b:= proc(n, i) option remember; `if`(i*(i+1)/2 b(n$2):
seq(a(n), n=0..100);  # Alois P. Heinz, Jun 02 2015

Mathematica

b[n_, i_] := b[n, i] = If[i*(i+1)/2Jean-François Alcover, Jan 15 2016, after Alois P. Heinz *)