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%I #38 Sep 03 2023 08:45:10
%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="https://doi.org/10.5937/SPSUNP1402091B">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.
%F Multiplicative with a(p^e) = (e+1)^4 - e^4. - _Amiram Eldar_, Sep 03 2023
%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)),","))
%o (PARI) a(n) = vecprod(apply(x->(x+1)^4-x^4, factor(n)[, 2])); \\ _Amiram Eldar_, Sep 03 2023
%Y Cf. A000005, A008683, A048691, A070919, A070921, A247516 (Mobius transform).
%K mult,easy,nonn
%O 1,2
%A _Benoit Cloitre_, May 20 2002
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