cp's OEIS Frontend

A240851 Number of partitions p of n into distinct parts not including mean(p).

%I A240851 #9 Sep 22 2023 01:58:52
%S A240851 0,0,0,1,1,2,2,4,5,5,9,11,10,17,21,21,27,37,40,53,50,69,88,103,98,126,
%T A240851 164,183,199,255,238,339,359,437,511,510,565,759,863,969,950,1259,
%U A240851 1224,1609,1750,1866,2303,2589,2497,3061,3412,4080,4485,5119,5168,6031
%N A240851 Number of partitions p of n into distinct parts not including mean(p).
%F A240851 a(n) + A240850(n) = A000009(n) for n >= 0.
%e A240851 a(9) counts these 5 partitions:  81, 72, 63. 621, 54.
%t A240851 z = 70; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
%t A240851 Table[Count[f[n], p_ /; MemberQ[p, Mean[p]]], {n, 0, z}]   (* A240850 *)
%t A240851 Table[Count[f[n], p_ /; ! MemberQ[p, Mean[p]]], {n, 0, z}] (* A240851 *)
%o A240851 (Python)
%o A240851 from sympy.utilities.iterables import partitions
%o A240851 def A240851(n): return sum(1 for s,p in partitions(n,size=True) if max(p.values(),default=0)==1 and (n%s or n//s not in p)) # _Chai Wah Wu_, Sep 21 2023
%Y A240851 Cf. A240850, A000009.
%K A240851 nonn,easy
%O A240851 0,6
%A A240851 _Clark Kimberling_, Apr 14 2014