OFFSET
1,3
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
J. R. Collis, On products of multiplicative functions, The Mathematical Gazette, Vol. 97, No. 539 (2013), pp. 263-264.
FORMULA
If n = Product_{i} p_i^e_i then a(n) = (sqrt(n) * Product_{i} (1 - 1/p_i)^(e_i/(e_i + 1))) ^ d(n), where d(n) is the number of divisors of n (Collis, 2013). - Amiram Eldar, Jun 16 2020
a(n) = Product_{k=1..n} phi(gcd(n,k))^(1/phi(n/gcd(n,k))) = Product_{k=1..n} phi(n/gcd(n,k))^(1/phi(n/gcd(n,k))). - Richard L. Ollerton, Nov 07 2021
MAPLE
seq(mul(numtheory:-phi(i), i=numtheory:-divisors(n)), n=1..100); # Robert Israel, Nov 21 2014
MATHEMATICA
Table[Product[EulerPhi[i], {i, Divisors[n]}], {n, 100}] (* Carl Najafi, Sep 06 2011 *)
PROG
(PARI) a(n) = my(d = divisors(n)); prod(k=1, #d, eulerphi(d[k])); \\ Michel Marcus, Nov 21 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Carl Najafi, Sep 06 2011
STATUS
approved