A337680 Number of distinct positive integer pairs, (s,t), such that s < t < n where neither s nor t divides n, and (t - s) | (t + s).

0, 0, 0, 0, 3, 1, 9, 5, 10, 11, 22, 9, 30, 25, 27, 29, 46, 28, 55, 37, 53, 62, 73, 43, 77, 80, 78, 76, 103, 69, 115, 95, 112, 121, 121, 91, 148, 143, 144, 121, 168, 132, 180, 161, 158, 191, 202, 149, 208, 192, 215, 210, 237, 193, 237, 215, 253, 262, 273, 197, 289, 284, 264, 272

Offset: 1

Author

Wesley Ivan Hurt, Sep 15 2020

Keywords

• nonn
• easy

Examples

			a(7) = 9; There are 9 positive integer pairs, (s,t), such that s < t < 7, neither s nor t divides 7, and where (t - s) | (t + s). They are (2,3), (2,4), (2,6), (3,4), (3,5), (3,6), (4,5), (4,6) and (5,6).
		

Crossrefs

Cf. A335567, A337273, A337588, A337679, A337681, A337682, 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((k+i)/(k-i)) + floor((k+i)/(k-i))).