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, 5, 9, 17, 21, 35, 39, 53, 61, 75, 79, 107, 111, 125, 139, 160, 164, 192, 196, 224, 238, 252, 256, 304, 312, 326, 340, 368, 372, 418, 422, 452, 466, 480, 494, 550, 554, 568, 582, 630, 634, 680, 684, 712, 740, 754, 758, 830, 838, 866, 880, 908, 912, 960, 974

Offset: 1

Author

Michel Marcus, Feb 13 2016

Keywords

• nonn

Comments

a(n) - a(n - 1) only depends on the prime signature of n. - David A. Corneth, Aug 30 2018

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000
• David A. Corneth, PARI prog
• Adrian W. Dudek, On the Success of Mishandling Euclid's Lemma, arXiv:1602.03555 [math.HO], 2016. See A(n) p. 2.
• Adrian W. Dudek, On the Success of Mishandling Euclid's Lemma, The American Mathematical Monthly, Vol. 123, No. 9 (2016), 924-927.

Crossrefs

Cf. A061502, A268732.

Programs

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;}

PARI

\\ See PARI link \\ David A. Corneth, Aug 30 2018