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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}.
2
1, 30, 30, 180, 30, 900, 30, 570, 180, 900, 30, 5400, 30, 900, 900, 1320, 30, 5400, 30, 5400, 900, 900, 30, 17100, 180, 900, 570, 5400, 30, 27000, 30, 2550, 900, 900, 900, 32400, 30, 900, 900, 17100, 30, 27000, 30, 5400, 5400, 900, 30, 39600, 180, 5400, 900
OFFSET
1,2
COMMENTS
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).
LINKS
O. Bagdasar, On Some Functions Involving the lcm and gcd of Integer Tuples, Scientific publications of the state university of Novi Pazar, Ser. A: Appl. Maths. Inform. and Mech., Vol. 6, 2 (2014), 91-100.
FORMULA
For n = p_1^{n_1} p_2^{n_2}...p_r^{n_r} one has
a(n) = Product_{i=1..r} ((n_i+1)^5 - 2*n_i^5 + (n_i-1)^5).
a(n) = 10^omega(n)*Product_{i=1..r} (2n_i^3 + n_i).
MATHEMATICA
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 *)
PROG
(PARI) a(n) = {f = factor(n); 10^omega(n)*prod(k=1, #f~, 2*f[k, 2]^3+f[k, 2]); }
CROSSREFS
L(n,2) produces A034444, A245019, A070921.
Cf. A247516.
Sequence in context: A186902 A185487 A051723 * A165851 A162503 A003896
KEYWORD
nonn,easy,mult
AUTHOR
Ovidiu Bagdasar, Sep 18 2014
STATUS
approved