%I #2 Mar 30 2012 17:31:17

%S 2,1,1,1,1,1,11,21,4,44,7,3,1,12,35,81,1429,2,132,22,8,6,154,7,21,21,

%T 8,6,29,434,6,91,4,900,15,1,126,66,14,11,122,4,477,3,481,77,4,27,15,

%U 612,600,56,4,4,8,3,44,71,310,217,6,3,74,132,333,2,1146,450,1655,186,58,3

%N Least number m, a multiple of n, such that P(m*n) is prime, where P(k) is the number of partitions of k.

%t Do[ PartitionsP[n], {n, 200000}]; f[n_] := Block[{k = 1}, While[ !PrimeQ[ PartitionsP[k*n]], k++ ]; k]; Array[f, 72]

%Y Cf. A000041, A046063, A114165, A111389, A111045, A114166, A111036, A114167, A114168, A114169, A114170, A114171.

%K nonn

%O 1,1

%A _Robert G. Wilson v_, Nov 14 2005