A337102 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.

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

Offset: 1

Author

Wesley Ivan Hurt, Aug 15 2020

Keywords

• nonn
• easy

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A004526, A337101.

Programs

Mathematica

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

Formula

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

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