A337681 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, 8, 3, 9, 9, 18, 6, 26, 22, 24, 22, 39, 23, 47, 31, 48, 54, 63, 30, 71, 71, 71, 64, 90, 60, 104, 82, 103, 109, 111, 74, 134, 130, 132, 103, 153, 121, 167, 149, 151, 177, 186, 122, 197, 181, 202, 194, 220, 180, 224, 194, 238, 244, 253, 167, 276, 272, 258, 253

Offset

1,5

Links

Table of n, a(n) for n=1..64.

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))).

Example

a(7) = 8; There are 8 distinct positive integer pairs, (s,t), such that s < t < 7, where neither s nor t divides 7 and (t - s) | (t * s). They are (2,3), (2,4), (2,6), (3,4), (3,6), (4,5), (4,6) and (5,6).

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}]

Crossrefs

Cf. A335567, A337273, A337588, A337679, A337680, A337682, A337683, A337684.

Sequence in context: A308742 A065451 A178148 * A245180 A054506 A101026

Adjacent sequences: A337678 A337679 A337680 * A337682 A337683 A337684

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Sep 15 2020

Status

approved