A200745 Number of partitions of n into distinct non-divisors of n.

1, 0, 0, 0, 0, 1, 0, 2, 1, 2, 2, 6, 1, 9, 5, 6, 5, 20, 4, 28, 7, 19, 24, 55, 6, 51, 45, 49, 27, 136, 16, 180, 50, 117, 143, 146, 28, 403, 242, 260, 68, 668, 91, 852, 246, 260, 649, 1370, 90, 1191, 493, 1110, 634, 2701, 386, 1635, 462, 2160, 2486, 5154, 167

Offset: 0

Author

Reinhard Zumkeller, Nov 22 2011

Keywords

• nonn

Examples

			a(10) = #{7+3, 6+4} = 2;
a(11) = #{9+2, 8+3, 7+4, 6+5, 6+3+2, 5+4+2} = 6;
a(12) = #{7+5} = 1;
a(13) = #{11+2, 10+3, 9+4, 8+5, 8+3+2, 7+6, 7+4+2, 6+5+2, 6+4+3} = 9;
a(14) = #{11+3, 10+4, 9+5, 8+6, 6+5+3} = 5;
a(15) = #{13+2, 11+5, 9+6, 9+4+2, 8+7, 8+5+2} = 6.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..2000 (terms 0..150 from Reinhard Zumkeller)

Crossrefs

Cf. A098743, A033630.

Programs

Haskell

a200745 n = p [nd | nd <- [1..n], mod n nd /= 0] n where
   p _  0 = 1
   p [] _ = 0
   p (k:ks) m | m < k = 0 | otherwise = p ks (m - k) + p ks m

Maple

a:= proc(n) option remember; local b, l;
      l:= sort([({$1..n} minus numtheory[divisors](n))[]]);
      b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
             b(n, i-1) +`if`(l[i]>n, 0, b(n-l[i], i-1))))
          end: forget(b):
      b(n, nops(l))
    end:
seq(a(n), n=0..80);  # Alois P. Heinz, Jan 18 2013

Mathematica

a[0] = 1; a[n_] := a[n] = Module[{b, l}, l = Sort[Range[n] ~Complement~ Divisors[n]]; b[m_, i_] := b[m, i] = If[m == 0, 1, If[i < 1, 0, b[m, i - 1] + If[l[[i]] > m, 0, b[m - l[[i]], i - 1]]]]; b[n, Length[l]]];
Table[a[n], {n, 0, 80}] (* Jean-François Alcover, Feb 06 2017, after Alois P. Heinz *)