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

0,8

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A098743, A033630.

Sequence in context: A284002 A093659 A306714 * A067541 A054706 A351082

Adjacent sequences: A200742 A200743 A200744 * A200746 A200747 A200748

Keyword

nonn

Author

Reinhard Zumkeller, Nov 22 2011

Status

approved