A337682 Number of distinct positive integer pairs, (s,t), such that s < t < n where neither s nor t divides n, and (s + t) | (s * t).

0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 3, 3, 2, 3, 4, 2, 5, 3, 5, 6, 6, 3, 7, 8, 6, 7, 9, 5, 12, 10, 11, 12, 11, 7, 15, 15, 14, 10, 17, 12, 19, 18, 14, 21, 21, 13, 22, 20, 22, 22, 23, 18, 23, 19, 25, 26, 26, 14, 31, 31, 26, 28, 31, 29, 34, 33, 33, 29, 36, 21, 39, 39, 34, 39, 39, 38

Offset: 1

Author

Wesley Ivan Hurt, Sep 15 2020

Keywords

• nonn
• easy

Examples

			a(13) = 3; There are 3 distinct positive integer pairs, (s,t), such that s < t < 13 where neither s nor t divides 13, and where (s + t) | (s * t). They are (3,6), (4,12) and (6,12).
		

Crossrefs

Cf. A335567, A337273, A337588, A337679, A337680, A337681, A337683, A337684.

Programs

Mathematica

Table[Sum[Sum[(1 - Ceiling[(i*k)/(k + i)] + Floor[(i*k)/(k + i)]) (Ceiling[n/k] - Floor[n/k]) (Ceiling[n/i] - Floor[n/i]), {i, k - 1}], {k, n}], {n, 100}]

Formula

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