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
Sum_{k>0} a(k)/k^s = (1/zeta(s))*Sum_{k>0} tau(k)^4/k^s.
Multiplicative with a(p^e) = (e+1)^4 - e^4. - Amiram Eldar, Sep 03 2023
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)), ", "))
(PARI) a(n) = vecprod(apply(x->(x+1)^4-x^4, factor(n)[, 2])); \\ Amiram Eldar, Sep 03 2023
CROSSREFS
KEYWORD
mult,easy,nonn
AUTHOR
Benoit Cloitre, May 20 2002
STATUS
approved