%I #7 Apr 16 2013 06:20:56

%S 4,5,6,9,12,17,22,30,39,52,67,89,114,149,191,247,314,403,509,647,813,

%T 1024,1278,1599,1983,2462,3037,3746,4594,5634,6873,8381,10176,12344,

%U 14918,18013,21674,26053,31224,37378,44624,53216,63304,75219

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

%C For n>2, k=a(n)-n.

%F 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 The partitions of a(4)=9 into k=9-4 parts are

%e 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 f[n_, k_] := Length[IntegerPartitions[n, {k}]]

%t t[n_] := Table[f[n, k] - k, {k, 1, n}]

%t b[n_] := Position[t[n], 0]

%t c = Flatten[Table[Last[b[n]], {n, 1, 60}]]

%t x = Flatten[Position[c, 1]]

%t y = Complement[Range[Length[x]], x]

%Y Cf. A000041, A133041.

%K nonn

%O 1,1

%A _Clark Kimberling_, Mar 05 2012