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A337684 Number of distinct positive integer pairs, (s,t), such that s < t < n where neither s, t, nor (s + t) divides n. 8
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 5 00:15 EDT 2021. Contains 346456 sequences. (Running on oeis4.)