OFFSET
1,3
FORMULA
a(n) = Product_{d|n} d^(phi(d)-phi(n/d)).
a(n) = n^n / Product_{d|n} d^(2*phi(n/d)).
a(n) = n^(-n) * Product_{d|n} d^(2*phi(d)).
a(n) = n^n / Product_{k=1..n} gcd(n,k)^2.
a(n) = n^(-n) * Product_{k=1..n} lcm(n,k)^2/k^2.
a(n) = A127553(n)/n!.
a(p) = p^(p-2), where p is a prime.
MATHEMATICA
Table[Product[LCM[n, k]/(k GCD[n, k]), {k, 1, n}], {n, 1, 23}]
Table[Product[d^(EulerPhi[d] - EulerPhi[n/d]), {d, Divisors[n]}], {n, 1, 23}]
PROG
(PARI) a(n) = prod(k=1, n, lcm(n, k)/(k*gcd(n, k))); \\ Michel Marcus, Jul 02 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 01 2019
STATUS
approved