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A070920 a(n) = Card{ (x,y,z,u) | lcm(x,y,z,u)=n }. 5
1, 15, 15, 65, 15, 225, 15, 175, 65, 225, 15, 975, 15, 225, 225, 369, 15, 975, 15, 975, 225, 225, 15, 2625, 65, 225, 175, 975, 15, 3375, 15, 671, 225, 225, 225, 4225, 15, 225, 225, 2625, 15, 3375, 15, 975, 975, 225, 15, 5535, 65, 975, 225, 975, 15, 2625, 225 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Antti Karttunen, 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, Appl. Maths. Inform. and Mech., Vol. 6, 2 (2014), 91--100.

FORMULA

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

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

MATHEMATICA

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

PROG

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

CROSSREFS

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

Sequence in context: A298044 A022349 A036379 * A056484 A056474 A219912

Adjacent sequences:  A070917 A070918 A070919 * A070921 A070922 A070923

KEYWORD

mult,easy,nonn

AUTHOR

Benoit Cloitre, May 20 2002

STATUS

approved

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Last modified December 5 11:35 EST 2021. Contains 349557 sequences. (Running on oeis4.)