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A100565 a(n) = Card{(x,y,z) : x <= y <= z, x|n, y|n, z|n, gcd(x,y)=1, gcd(x,z)=1, gcd(y,z)=1}. 1
1, 2, 2, 3, 2, 5, 2, 4, 3, 5, 2, 8, 2, 5, 5, 5, 2, 8, 2, 8, 5, 5, 2, 11, 3, 5, 4, 8, 2, 15, 2, 6, 5, 5, 5, 13, 2, 5, 5, 11, 2, 15, 2, 8, 8, 5, 2, 14, 3, 8, 5, 8, 2, 11, 5, 11, 5, 5, 2, 25, 2, 5, 8, 7, 5, 15, 2, 8, 5, 15, 2, 18, 2, 5, 8, 8, 5, 15, 2, 14, 5, 5, 2, 25, 5, 5, 5, 11, 2, 25, 5, 8, 5, 5, 5, 17 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also a(n) = Card{(x,y,z) : x <= y <= z and lcm(x,y)=n, lcm(x,z)=n, lcm(y,z)=n}.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = (tau(n^3) + 3*tau(n) + 2)/6.

PROG

(PARI) A100565(n) = (numdiv(n^3)+3*numdiv(n)+2)/6; \\ Antti Karttunen, May 19 2017

CROSSREFS

Cf. A000005, A048785, A066620, A070919, A086222, A086165, A048691, A018892, A063647.

Sequence in context: A141822 A033099 A018892 * A244098 A285573 A325339

Adjacent sequences:  A100562 A100563 A100564 * A100566 A100567 A100568

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Nov 28 2004

STATUS

approved

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Last modified April 23 07:51 EDT 2019. Contains 322381 sequences. (Running on oeis4.)