cp's OEIS Frontend

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

%I A200745 #24 Nov 03 2023 10:28:35
%S A200745 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,
%T A200745 136,16,180,50,117,143,146,28,403,242,260,68,668,91,852,246,260,649,
%U A200745 1370,90,1191,493,1110,634,2701,386,1635,462,2160,2486,5154,167
%N A200745 Number of partitions of n into distinct non-divisors of n.
%H A200745 Alois P. Heinz, <a href="/A200745/b200745.txt">Table of n, a(n) for n = 0..2000</a> (terms 0..150 from Reinhard Zumkeller)
%e A200745 a(10) = #{7+3, 6+4} = 2;
%e A200745 a(11) = #{9+2, 8+3, 7+4, 6+5, 6+3+2, 5+4+2} = 6;
%e A200745 a(12) = #{7+5} = 1;
%e A200745 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;
%e A200745 a(14) = #{11+3, 10+4, 9+5, 8+6, 6+5+3} = 5;
%e A200745 a(15) = #{13+2, 11+5, 9+6, 9+4+2, 8+7, 8+5+2} = 6.
%p A200745 a:= proc(n) option remember; local b, l;
%p A200745       l:= sort([({$1..n} minus numtheory[divisors](n))[]]);
%p A200745       b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A200745              b(n, i-1) +`if`(l[i]>n, 0, b(n-l[i], i-1))))
%p A200745           end: forget(b):
%p A200745       b(n, nops(l))
%p A200745     end:
%p A200745 seq(a(n), n=0..80);  # _Alois P. Heinz_, Jan 18 2013
%t A200745 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]]];
%t A200745 Table[a[n], {n, 0, 80}] (* _Jean-François Alcover_, Feb 06 2017, after _Alois P. Heinz_ *)
%o A200745 (Haskell)
%o A200745 a200745 n = p [nd | nd <- [1..n], mod n nd /= 0] n where
%o A200745    p _  0 = 1
%o A200745    p [] _ = 0
%o A200745    p (k:ks) m | m < k = 0 | otherwise = p ks (m - k) + p ks m
%Y A200745 Cf. A098743, A033630.
%K A200745 nonn
%O A200745 0,8
%A A200745 _Reinhard Zumkeller_, Nov 22 2011