OFFSET
1,2
COMMENTS
The Dirichlet convolution of a(n) and sigma(n) is sigma(n^2).
LINKS
Álvar Ibeas, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = n^2 * Sum_{d^2 | n} (moebius(d) / d^2).
Multiplicative with a(p) = p^2; a(p^e) = p^(2e) - p^(2e-2), for e > 1.
Dirichlet g.f.: zeta(s-2) / zeta(2s-2).
Sum_{k=1..n} a(k) ~ 30 * n^3 / Pi^4. - Vaclav Kotesovec, Jan 11 2019
Sum_{k>=1} 1/a(k) = Product_{primes p} (1 + 1/p^2 + 1/(p^2 - 1)^2) = 1.681923034881403168503816690236967736500606659628336043348190538886262268... - Vaclav Kotesovec, Sep 20 2020
PROG
(PARI) a(n) = n^2*sumdiv(n, d, if (issquare(d), moebius(sqrtint(d))/d)); \\ Michel Marcus, Feb 10 2015
CROSSREFS
KEYWORD
mult,nonn
AUTHOR
Álvar Ibeas, Jan 31 2015
STATUS
approved