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%I #14 Jan 16 2014 04:48:40
%S 1,1,1,14,1,5,1,7,15,3,1,66,286,3,1,11,22715,44,33,35761,2,1,363,33,
%T 63,143,5,2,84,1,2425,72610,7,2725580,11,22,926026,3283,123981330,
%U 58088,363,1,70,4,3,176484,11209,85166,10,141790,11209835405
%N a(n) is the smallest number k such that n*k is a partition number.
%C a(n) = 1 iff n is a partition number.
%F a(n) = A072871(n)/n.
%e For n = 4, a(4) = 14 because if 1<=k<=13 we have that 4*k is not a partition number, but if k = 14 then 4*14 = 56 and 56 is the number of partitions of 11.
%t a[n_] := PartitionsP[NestWhile[(# + 1)&, 1, Mod[PartitionsP@ #, n] > 0 &]]/n; Array[a,51] (* _Giovanni Resta_, Jan 15 2014 *)
%Y Cf. A000041, A046641, A072871, A213179, A213365, A216258, A217725, A217726, A222175, A222178, A222179, A225317, A225361.
%K nonn
%O 1,4
%A _Omar E. Pol_, Jan 14 2014