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A247516 Card{(x,y,z,t): 1<=x,y,z,t<=n, gcd(x,y,z,t)=1, lcm(x,y,z,t)=n}. 3
1, 14, 14, 50, 14, 196, 14, 110, 50, 196, 14, 700, 14, 196, 196, 194, 14, 700, 14, 700, 196, 196, 14, 1540, 50, 196, 110, 700, 14, 2744, 14, 302, 196, 196, 196, 2500, 14, 196, 196, 1540, 14, 2744, 14, 700, 700, 196, 14, 2716, 50, 700, 196, 700, 14, 1540, 196 (list; graph; refs; listen; history; text; internal format)
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,4).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

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)^4 - 2*n_i^4 + (n_i-1)^4).

a(n) = 2^omega(n)*Product_{i=1..r} (6n_i^2 + 1).

PROG

(PARI) a(n) = {f = factor(n); 2^omega(n)*prod(k=1, #f~, 6*f[k, 2]^2+1); } \\ Michel Marcus, Sep 18 2014

CROSSREFS

Cf. A034444 (produced by L(n,2)), A245019, A070920.

Sequence in context: A022348 A214463 A006662 * A135820 A165835 A134913

Adjacent sequences:  A247513 A247514 A247515 * A247517 A247518 A247519

KEYWORD

nonn,mult

AUTHOR

Ovidiu Bagdasar, Sep 18 2014

EXTENSIONS

More terms from Michel Marcus, Sep 18 2014

STATUS

approved

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Last modified March 20 13:18 EDT 2019. Contains 321345 sequences. (Running on oeis4.)