cp's OEIS Frontend

A316854 Number of integer partitions of n whose reciprocal sum is the reciprocal of an integer.

%I A316854 #20 Sep 03 2018 16:30:55
%S A316854 1,1,1,2,1,1,1,2,3,2,2,2,1,1,1,4,2,4,1,5,1,5,1,3,4,2,5,6,5,5,4,5,5,4,
%T A316854 8,10,9,7,5,9,10,6,12,10,8,7,6,9,13,15,8,19,13,19,19,19,18,22,26,28,
%U A316854 28,29,22,33,29,28,38,34,26,40,32,43,39,51,38,62,46
%N A316854 Number of integer partitions of n whose reciprocal sum is the reciprocal of an integer.
%C A316854 The reciprocal sum of (y_1, ..., y_k) is 1/y_1 + ... + 1/y_k.
%H A316854 Giovanni Resta, <a href="/A316854/b316854.txt">Table of n, a(n) for n = 1..200</a> (first 100 terms from Robert G. Wilson v)
%e A316854 The a(36) = 10 partitions:
%e A316854   (36),
%e A316854   (30,6), (24,12), (18,18),
%e A316854   (12,12,12),
%e A316854   (12,12,6,6),
%e A316854   (15,10,4,4,3), (12,12,6,3,3), (12,8,8,6,2),
%e A316854   (6,6,6,6,6,6).
%t A316854 Table[Length[Select[IntegerPartitions[n],IntegerQ[1/Sum[1/m,{m,#}]]&]],{n,30}]
%t A316854 ric[n_, p_, s_] := If[n == 0, If[IntegerQ[1/s], c++], Do[If[s + 1/i <= 1, ric[n - i, Append[p, i], s + 1/i]], {i, Min[p[[-1]], n], 1, -1}]]; a[n_] := (c = 0; Do[ric[n - j, {j}, 1/j], {j, n}]; c); Array[a, 80] (* after Giovanni Resta in A316898, _Robert G. Wilson v_, Jul 23 2018 *)
%o A316854 (PARI) a(n)={my(s=0); forpart(p=n, if(frac(1/sum(i=1, #p, 1/p[i]))==0, s++)); s} \\ _Andrew Howroyd_, Jul 15 2018
%Y A316854 Cf. A000041, A051908, A058360, A316855, A316856, A316857.
%K A316854 nonn
%O A316854 1,4
%A A316854 _Gus Wiseman_, Jul 14 2018
%E A316854 a(51)-a(77) from _Giovanni Resta_, Jul 15 2018