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A335567 Number of distinct positive integer pairs, (s,t), such that s <= t < n where neither s nor t divides n. 8
0, 0, 1, 1, 6, 3, 15, 10, 21, 21, 45, 21, 66, 55, 66, 66, 120, 78, 153, 105, 153, 171, 231, 136, 253, 253, 276, 253, 378, 253, 435, 351, 435, 465, 496, 378, 630, 595, 630, 528, 780, 595, 861, 741, 780, 903, 1035, 741, 1081, 990, 1128, 1081, 1326, 1081, 1326, 1176, 1431 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Table of n, a(n) for n=1..57.

FORMULA

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

EXAMPLE

a(7) = 15; There are 5 positive integers less than 7 that do not divide 7, {2,3,4,5,6}. From this list, there are 15 ordered pairs, (s,t), such that s <= t < 7. They are (2,2), (2,3), (2,4), (2,5), (2,6), (3,3), (3,4), (3,5), (3,6), (4,4), (4,5), (4,6), (5,5), (5,6) and (6,6). So a(7) = 15.

MATHEMATICA

Table[Sum[Sum[(Ceiling[n/k] - Floor[n/k]) (Ceiling[n/i] - Floor[n/i]), {i, k}], {k, n}], {n, 100}]

CROSSREFS

Cf. A337273, A337588, A337679, A337680, A337681, A337682, A337683, A337684.

Sequence in context: A341746 A097917 A116570 * A225503 A302350 A046879

Adjacent sequences:  A335564 A335565 A335566 * A335568 A335569 A335570

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Sep 14 2020

STATUS

approved

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Last modified September 16 05:49 EDT 2021. Contains 347469 sequences. (Running on oeis4.)