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A239509 Number of partitions of n into distinct nonprime squarefree numbers, cf. A000469. 5
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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: A051168 A281459 A163528 * A258747 A160806 A287385

Adjacent sequences:  A239506 A239507 A239508 * A239510 A239511 A239512

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Mar 21 2014

STATUS

approved

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Last modified October 17 02:14 EDT 2018. Contains 316275 sequences. (Running on oeis4.)