%I
%S 0,1,0,0,1,0,1,0,2,2,4,0,9,0,8,11,15,0,39,0,44,45,28,0,175,30,50,146,
%T 207,0,486,0,427,415,144,378,1736,0,236,1084,2669,0,3022,0,3279,4977,
%U 600,0,12557,1195,6503,5959,11042,0,17047,12549,25925,12977,2174
%N Number of partitions p of n such that the multiplicity of the mean of p is a part of p.
%C a(n) = 0 if and only if n is a prime or 0.
%e a(1) counts these 4 partitions: 52111, 42211, 33211, 32221.
%t z = 60; f[n_] := f[n] = IntegerPartitions[n];
%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, Mean[p]]]], {n, 0, z}] (* A240491 *)
%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, Median[p]]]], {n, 0, z}] (* A240492 *)
%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, Min[p]]]], {n, 0, z}] (* A240493 *)
%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, Max[p]]]], {n, 0, z}] (* A240494 *)
%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, Max[p]  Min[p]]]], {n, 0, z}] (* A240495 *)
%Y Cf. A240491  A240494.
%K nonn,easy
%O 0,9
%A _Clark Kimberling_, Apr 06 2014
