cp's OEIS Frontend

A209122 Numbers a(n) for which there exists k>1 such that the number of partitions of a(n) into k parts is k.

%I A209122 #7 Apr 16 2013 06:20:56
%S A209122 4,5,6,9,12,17,22,30,39,52,67,89,114,149,191,247,314,403,509,647,813,
%T A209122 1024,1278,1599,1983,2462,3037,3746,4594,5634,6873,8381,10176,12344,
%U A209122 14918,18013,21674,26053,31224,37378,44624,53216,63304,75219
%N A209122 Numbers a(n) for which there exists k>1 such that the number of partitions of a(n) into k parts is k.
%C A209122 For n>2, k=a(n)-n.
%F A209122 a(1)=4, a(2)=5, and a(n)=n+A000041(n) if n>2; i.e., k(n)=A000041(n) for n>2.
%e A209122 The partitions of a(4)=9 into k=9-4 parts are
%e A209122 5+1+1+1+1, 4+2+1+1+1, 3+3+1+1+1, 3+2+3+1+1, 2+2+2+2+1.
%t A209122 f[n_, k_] := Length[IntegerPartitions[n, {k}]]
%t A209122 t[n_] := Table[f[n, k] - k, {k, 1, n}]
%t A209122 b[n_] := Position[t[n], 0]
%t A209122 c = Flatten[Table[Last[b[n]], {n, 1, 60}]]
%t A209122 x = Flatten[Position[c, 1]]
%t A209122 y = Complement[Range[Length[x]], x]
%Y A209122 Cf. A000041, A133041.
%K A209122 nonn
%O A209122 1,1
%A A209122 _Clark Kimberling_, Mar 05 2012