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A070920 a(n) = Card{ (x,y,z,u) | lcm(x,y,z,u)=n }. 5

%I

%S 1,15,15,65,15,225,15,175,65,225,15,975,15,225,225,369,15,975,15,975,

%T 225,225,15,2625,65,225,175,975,15,3375,15,671,225,225,225,4225,15,

%U 225,225,2625,15,3375,15,975,975,225,15,5535,65,975,225,975,15,2625,225

%N a(n) = Card{ (x,y,z,u) | lcm(x,y,z,u)=n }.

%C A048691(n) gives Card{ (x,y) | lcm(x,y)=n }.

%H Antti Karttunen, <a href="/A070920/b070920.txt">Table of n, a(n) for n = 1..10000</a>

%H O. Bagdasar, <a href="http://www.np.ac.rs/downloads/publications/VOL6_Br_2/vol6br2-3.pdf">On some functions involving the lcm and gcd of integer tuples</a>, Scientific Publications of the State University of Novi Pazar, Appl. Maths. Inform. and Mech., Vol. 6, 2 (2014), 91--100.

%F a(n) = Sum_{d|n} A000005(d)^4*A008683(n/d).

%F Sum_{k>0} a(k)/k^s = (1/zeta(s))*Sum_{k>0} tau(k)^4/k^s.

%t Join[{1},Table[Product[(k + 1)^4 - k^4, {k, FactorInteger[n][[All, 2]]}], {n,2, 68}]] (* _Geoffrey Critzer_, Jan 10 2015 *)

%o (PARI) for(n=1,100,print1(sumdiv(n,d,numdiv(d)^4*moebius(n/d)),","))

%Y Cf. A048691, A070919, A070921, A247516 (Mobius transform?).

%K mult,easy,nonn

%O 1,2

%A _Benoit Cloitre_, May 20 2002

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Last modified February 21 01:29 EST 2019. Contains 320364 sequences. (Running on oeis4.)