cp's OEIS Frontend

A247517 Card{(x,y,z,t,u): 1<=x,y,z,t,u<=n, gcd(x,y,z,t,u)=1, lcm(x,y,z,t,u)=n}.

%I A247517 #29 Sep 03 2023 08:44:32
%S A247517 1,30,30,180,30,900,30,570,180,900,30,5400,30,900,900,1320,30,5400,30,
%T A247517 5400,900,900,30,17100,180,900,570,5400,30,27000,30,2550,900,900,900,
%U A247517 32400,30,900,900,17100,30,27000,30,5400,5400,900,30,39600,180,5400,900
%N A247517 Card{(x,y,z,t,u): 1<=x,y,z,t,u<=n, gcd(x,y,z,t,u)=1, lcm(x,y,z,t,u)=n}.
%C A247517 For given n and k positive integers, let L(n,k) represent the number of ordered k-tuples of positive integers, whose GCD is 1 and LCM is n. In this notation, the sequence corresponds to a(n) = L(n,5).
%H A247517 Antti Karttunen, <a href="/A247517/b247517.txt">Table of n, a(n) for n = 1..10000</a>
%H A247517 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, Ser. A: Appl. Maths. Inform. and Mech., Vol. 6, 2 (2014), 91-100.
%F A247517 For n = p_1^{n_1} p_2^{n_2}...p_r^{n_r} one has
%F A247517 a(n) = Product_{i=1..r} ((n_i+1)^5 - 2*n_i^5 + (n_i-1)^5).
%F A247517 a(n) = 10^omega(n)*Product_{i=1..r} (2n_i^3 + n_i).
%t A247517 f[p_, e_] := 10*(2*e^3 + e); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Sep 03 2023 *)
%o A247517 (PARI) a(n) = {f = factor(n); 10^omega(n)*prod(k=1, #f~, 2*f[k, 2]^3+f[k, 2]); }
%Y A247517 L(n,2) produces A034444, A245019, A070921.
%Y A247517 Cf. A247516.
%K A247517 nonn,easy,mult
%O A247517 1,2
%A A247517 _Ovidiu Bagdasar_, Sep 18 2014