OFFSET
1,3
COMMENTS
LINKS
Ridouane Oudra, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = Sum_{d|n} f(d) * phi(n/d), where f(n) = A014963(n) - 1.
a(n) = Sum_{d|n, d is a prime power} A057237(d) * phi(n/d).
a(n) is neither multiplicative nor additive, but it satisfies the mixed relation:
a(n*m) = phi(n) * a(m) + phi(m) * a(n), for all n, m such that gcd(n,m) = 1.
Dirichlet g.f.: zeta(s-1)/zeta(s) * Sum_{p prime} (p-1)/(p^s-1).
EXAMPLE
a(30) = phi(30)*omega(30) = 8*3 = 24.
MAPLE
with(numtheory): seq(phi(n)*nops(factorset(n)), n=1..120);
MATHEMATICA
Table[EulerPhi[n]*PrimeNu[n], {n, 1, 120}]
PROG
(PARI) a(n) = my(f=factor(n)); eulerphi(f)*omega(f); \\ Michel Marcus, Nov 12 2025
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ridouane Oudra, Nov 12 2025
STATUS
approved
