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A308944 a(n) = Product_{k=1..n} lcm(n,k) / (k * gcd(n,k)). 0
1, 1, 3, 4, 125, 9, 16807, 1024, 59049, 15625, 2357947691, 5184, 1792160394037, 282475249, 474609375, 17179869184, 2862423051509815793, 3486784401, 5480386857784802185939, 250000000000, 10382917022245341, 5559917313492231481, 39471584120695485887249589623 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..23.

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(n) = A056916(n)/A067911(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

Cf. A000010, A051190, A056916, A067911, A071248, A119619, A127553.

Sequence in context: A041465 A004124 A175504 * A280735 A290282 A331815

Adjacent sequences:  A308941 A308942 A308943 * A308945 A308946 A308947

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jul 01 2019

STATUS

approved

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Last modified May 8 23:53 EDT 2021. Contains 343685 sequences. (Running on oeis4.)