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

1,5

Links

Table of n, a(n) for n=1..78.

Index entries for sequences related to partitions

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).

Mathematica

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

Crossrefs

Cf. A004526, A337101.

Sequence in context: A308048 A335967 A319611 * A239495 A348163 A298210

Adjacent sequences: A337099 A337100 A337101 * A337103 A337104 A337105

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Aug 15 2020

Status

approved