OFFSET
1,2
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
Multiplicative with a(p^e) = p^e*(p^e - p^(e-1)) + (p^(2*e) - 1)/(p^2 - 1). - Amiram Eldar, Sep 15 2019
Sum_{k=1..n} a(k) ~ c * n^3, where c = (zeta(3)/3) * Product_{p prime} (1 - 1/p^2 + 1/p^5) = 0.2550149528... . - Amiram Eldar, Oct 28 2022
MAPLE
for i from 1 to 100 do d := divisors(i): a[i] := i*phi(i)*sum(1/d[j]/phi(d[j]), j=1..nops(d)) od:seq(a[j], j=1..100);
MATHEMATICA
f[p_, e_] := p^e*(p^e - p^(e-1)) + (p^(2*e) - 1)/(p^2 - 1) ; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Sep 15 2019 *)
PROG
(Magma) [&+[(n div d)*EulerPhi(n) div EulerPhi(d):d in Divisors(n)]:n in [1..52]]; // Marius A. Burtea, Sep 15 2019
(PARI) a(n) = sumdiv(n, d, n/d*eulerphi(n)/eulerphi(d)); \\ Michel Marcus, Sep 15 2019
CROSSREFS
KEYWORD
mult,easy,nonn
AUTHOR
Vladeta Jovovic, Apr 10 2002
EXTENSIONS
More terms from Sascha Kurz, Jan 03 2003
STATUS
approved