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A070921 a(n) = Card{ (x,y,z,u,v) | lcm(x,y,z,u,v)=n }. 5
1, 31, 31, 211, 31, 961, 31, 781, 211, 961, 31, 6541, 31, 961, 961, 2101, 31, 6541, 31, 6541, 961, 961, 31, 24211, 211, 961, 781, 6541, 31, 29791, 31, 4651, 961, 961, 961, 44521, 31, 961, 961, 24211, 31, 29791, 31, 6541, 6541, 961, 31, 65131, 211, 6541 (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)^5*A008683(n/d).

Sum_{k>0} a(k)/k^s = (1/zeta(s))*Sum_{k>0} tau(k)^5/k^s.

MATHEMATICA

Join[{1}, Table[Product[(k + 1)^5 - k^5, {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)^5*moebius(n/d)), ", "))

CROSSREFS

Cf. A048691, A070919, A070920, A247517 (Mobius transform?).

Sequence in context: A140718 A040931 A022365 * A165852 A291523 A256496

Adjacent sequences:  A070918 A070919 A070920 * A070922 A070923 A070924

KEYWORD

mult,easy,nonn

AUTHOR

Benoit Cloitre, May 20 2002

STATUS

approved

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Last modified January 17 19:58 EST 2019. Contains 319251 sequences. (Running on oeis4.)