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A268756 Number of triples x, y, r such that r divides x*y, r divides at least one of x or y, and x*y <= n. 1

%I #18 Jan 09 2019 03:56:01

%S 1,5,9,17,21,35,39,53,61,75,79,107,111,125,139,160,164,192,196,224,

%T 238,252,256,304,312,326,340,368,372,418,422,452,466,480,494,550,554,

%U 568,582,630,634,680,684,712,740,754,758,830,838,866,880,908,912,960,974

%N Number of triples x, y, r such that r divides x*y, r divides at least one of x or y, and x*y <= n.

%C a(n) - a(n - 1) only depends on the prime signature of n. - _David A. Corneth_, Aug 30 2018

%H David A. Corneth, <a href="/A268756/b268756.txt">Table of n, a(n) for n = 1..10000</a>

%H David A. Corneth, <a href="/A268756/a268756.gp.txt">PARI prog</a>

%H Adrian W. Dudek, <a href="http://arxiv.org/abs/1602.03555">On the Success of Mishandling Euclid's Lemma</a>, arXiv:1602.03555 [math.HO], 2016. See A(n) p. 2.

%H Adrian W. Dudek, <a href="https://doi.org/10.4169/amer.math.monthly.123.9.924">On the Success of Mishandling Euclid's Lemma</a>, The American Mathematical Monthly, Vol. 123, No. 9 (2016), 924-927.

%o (PARI) a(n) = {s = 0; for (x=1, n, for (y = 1, n, if (x*y <= n, s += sum(r = 1, x*y, !(x*y % r) && (!(x % r) || !(y % r)));););); s;}

%o (PARI) \\ See PARI link \\ _David A. Corneth_, Aug 30 2018

%Y Cf. A061502, A268732.

%K nonn

%O 1,2

%A _Michel Marcus_, Feb 13 2016

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)