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

0,16

Links

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

Example

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.

Maple

b:= proc(n, i) option remember; `if`(i*(i+1)/2<n, 0,
      `if`(n=0, 1, b(n, i-1) +`if`(i<=n and not
      isprime(i) and issqrfree(i), b(n-i, i-1), 0)))
    end:
a:= n-> 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)/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 *)

Prog

(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

Crossrefs

Cf. A239508, A087188.

Sequence in context: A281459 A163528 A329054 * A360985 A335833 A258747

Adjacent sequences: A239506 A239507 A239508 * A239510 A239511 A239512

Keyword

nonn

Author

Reinhard Zumkeller, Mar 21 2014

Status

approved