A337684 Number of distinct positive integer pairs, (s,t), such that s < t < n where neither s, t, nor (s + t) divides n.

0, 0, 0, 0, 2, 1, 8, 5, 13, 13, 32, 14, 50, 40, 51, 50, 98, 61, 128, 85, 128, 142, 200, 114, 220, 217, 241, 219, 338, 221, 392, 309, 390, 415, 449, 337, 578, 538, 575, 478, 722, 540, 800, 677, 720, 832, 968, 680, 1011, 916, 1053, 1002, 1250, 1002, 1247, 1096, 1346, 1393, 1568

Offset

1,5

Links

Table of n, a(n) for n=1..59.

Formula

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

Example

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

Mathematica

Table[Sum[Sum[(Ceiling[n/(k + i)] - Floor[n/(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, A337588, A337679, A337680, A337681, A337682, A337683.

Sequence in context: A298592 A344163 A199468 * A004732 A297809 A160641

Adjacent sequences: A337681 A337682 A337683 * A337685 A337686 A337687

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Sep 15 2020

Status

approved