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

Author

Wesley Ivan Hurt, Sep 15 2020

Keywords

• nonn
• easy

Examples

			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).
		

Crossrefs

Cf. A335567, A337273, A337588, A337679, A337680, A337681, A337682, A337683.

Programs

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}]

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))).