OFFSET
1,2
COMMENTS
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
Multiplicative with a(p^e) = 2*(-p)^e (p prime, e>0).
Dirichlet inverse of abs(a(n)).
Dirichlet g.f.: zeta(2*s-2)/(zeta(s-1))^2.
O.g.f. for the unsigned sequence: Sum_{n >= 1} |a(n)|*x^n = Sum_{n >= 1} |mu(n)|*n*x^n/(1 - x^n)^2, where mu(n) = A008683(n) is the Möbius function. - Peter Bala, Mar 05 2022
EXAMPLE
a(6) = a(2)*a(3) = (-4)*(-6) = 24 = 6*1*2^2;
a(8) = a(2^3) = 2*(-2)^3 = -16 = 8*(-1)*2^1.
MAPLE
f:= proc(n) local t;
mul(2*(-t[1])^t[2], t=ifactors(n)[2])
end proc:
map(f, [$1..100]); # Robert Israel, Mar 06 2022
MATHEMATICA
Array[# (-1)^PrimeOmega[#]*2^PrimeNu[#] &, 60] (* Michael De Vlieger, Jan 20 2018 *)
PROG
(PARI) a(n) = n*(-1)^bigomega(n)*2^omega(n); \\ Michel Marcus, Jan 20 2018
CROSSREFS
KEYWORD
sign,mult
AUTHOR
Werner Schulte, Jan 19 2018
STATUS
approved