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Number of partitions of n into two positive integer parts (s,t), s<=t, such that the harmonic mean of the smallest and largest part is not an integer.
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%I #6 Feb 01 2021 21:25:42

%S 0,0,1,1,2,2,3,2,3,4,5,5,6,6,7,6,8,6,9,9,10,10,11,10,10,12,12,13,14,

%T 14,15,12,16,16,17,15,18,18,19,18,20,20,21,21,21,22,23,22,21,20,25,25,

%U 26,24,27,26,28,28,29,29,30,30,30,28,32,32,33,33,34,34,35,30,36,36,35,37,38,38

%N Number of partitions of n into two positive integer parts (s,t), s<=t, such that the harmonic mean of the smallest and largest part is not an integer.

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F a(n) = Sum_{i=1..floor(n/2)} (ceiling(2*i*(n-i)/n) - floor(2*i*(n-i)/n)).

%F a(n) = A004526(n) - A337101(n).

%t Table[Sum[Ceiling[2*i*(n - i)/n] - Floor[2*i*(n - i)/n], {i, Floor[n/2]}], {n, 100}]

%Y Cf. A004526, A337101.

%K nonn,easy

%O 1,5

%A _Wesley Ivan Hurt_, Aug 15 2020