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 A240491 Number of partitions p of n such that the multiplicity of the mean of p is a part of p. 5

%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

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Last modified May 16 03:58 EDT 2022. Contains 353688 sequences. (Running on oeis4.)