A337588 Number of distinct positive integer pairs, (s,t), such that s < t < n where neither s nor t divides n, but s | t.

0, 0, 0, 0, 1, 0, 3, 1, 4, 3, 8, 1, 12, 7, 10, 8, 19, 7, 23, 10, 21, 20, 31, 8, 34, 27, 32, 23, 46, 17, 52, 30, 46, 43, 52, 22, 69, 52, 59, 36, 79, 38, 85, 54, 65, 72, 95, 36, 98, 70, 92, 73, 114, 61, 108, 71, 110, 103, 132, 45, 142, 113, 112, 96, 139, 90, 161, 112, 143

Offset

1,7

Links

Table of n, a(n) for n=1..69.

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) + floor(k/i)).

Example

a(11) = 8; There are 9 positive integers less than 11 that do not divide 11, {2,3,4,5,6,7,8,9,10}. Of these, there are 8 ordered pairs, (s,t), where s < t < 11 and s | t. They are (2,4), (2,6), (2,8), (2,10), (3,6), (3,9), (4,8) and (5,10).

Mathematica

Table[Sum[Sum[(1 - Ceiling[k/i] + Floor[k/i]) (Ceiling[n/k] - Floor[n/k])(Ceiling[n/i] - Floor[n/i]), {i, k - 1}], {k, n}], {n, 80}]

Crossrefs

Cf. A335567, A337273, A337679, A337680, A337681, A337682, A337683, A337684.

Sequence in context: A364670 A060043 A298254 * A364272 A316402 A054907

Adjacent sequences: A337585 A337586 A337587 * A337589 A337590 A337591

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Sep 15 2020

Status

approved