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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

%I

%S 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,

%T 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,

%U 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

%N 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}.

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

%H Antti Karttunen, <a href="/A100565/b100565.txt">Table of n, a(n) for n = 1..10000</a>

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

%o (PARI) A100565(n) = (numdiv(n^3)+3*numdiv(n)+2)/6; \\ _Antti Karttunen_, May 19 2017

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

%K easy,nonn

%O 1,2

%A _Vladeta Jovovic_, Nov 28 2004

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Last modified September 23 08:18 EDT 2020. Contains 337295 sequences. (Running on oeis4.)