OFFSET
1,2
COMMENTS
Inverse Möbius transform of n * phi(n) * mu(n)^2.
LINKS
N. J. A. Sloane, Transforms.
FORMULA
Multiplicative with a(p^e) = p^2 - p + 1. - Amiram Eldar, Dec 04 2023
Sum_{k=1..n} a(k) ~ c * n^3/3, where c = Product_{p prime} (1 - 2/(1+p+p^2)) = 0.51478027457383523467921514707014858470711969900467102074735896602342984... - Vaclav Kotesovec, Dec 05 2023
MATHEMATICA
Table[Sum[d*EulerPhi[d]*MoebiusMu[d]^2, {d, Divisors[n]}], {n, 100}]
PROG
(PARI) a(n) = sumdiv(n, d, if (issquarefree(d), d*eulerphi(d))); \\ Michel Marcus, Dec 04 2023
(Python)
from math import prod
from sympy import primefactors
def A367865(n): return prod(p*(p-1)+1 for p in primefactors(n)) # Chai Wah Wu, Dec 05 2023
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Wesley Ivan Hurt, Dec 03 2023
STATUS
approved