OFFSET
1,3
COMMENTS
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = n * Sum_{d|n} A076479(d)/d.
Sum_{k=1..n} a(k) ~ A065469 * n*(n+1)/2.
Multiplicative with a(p^e) = p^e - (p^e - 1)/(p-1).
a(n) = Sum_{d|n} mu(d)*tau(d)*sigma(n/d). - Ridouane Oudra, Nov 24 2019
a(n) = Sum_{d|n} A058026(d). - Amiram Eldar, May 01 2020
MAPLE
with(numtheory): omega := n -> nops(factorset(n)):
seq(add((-1)^omega(n/d)*d, d in divisors(n)), n=1..100); # Ridouane Oudra, Nov 24 2019
MATHEMATICA
f[p_, e_] := p^e - (p^e - 1)/(p - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, May 01 2020 *)
PROG
(PARI) a(n) = sumdiv(n, d, (-1)^omega(n/d) * d);
(PARI) a(n) = my(f=factor(n)); prod(k=1, #f~, f[k, 1]^f[k, 2] - (f[k, 1]^f[k, 2] - 1)/(f[k, 1]-1));
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Daniel Suteu, Apr 05 2019
STATUS
approved