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A334489 a(n) = Product_{d|n} (pod(n)/pod(d)) where pod(n) = A007955(n), the product of divisors of n. 0
1, 2, 3, 32, 5, 7776, 7, 16384, 243, 100000, 11, 8916100448256, 13, 537824, 759375, 1073741824, 17, 1156831381426176, 19, 4096000000000000, 4084101, 5153632, 23, 2315513501476187716057433112576, 3125, 11881376, 4782969, 232218265089212416, 29 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..29.

FORMULA

a(p) = p for p = primes (A000040).

a(n) = ((lcm_{d|n} pod(d))^tau(n)) / Product_{d|n} (pod(d)) = A007955(n)^A000005(n)/A266265(n).

a(n) = n^c(n) where c(n) only depends on the prime signature of n. - David A. Corneth, May 05 2020

EXAMPLE

For n = 6; divisors d of 6: {1, 2, 3, 6}; pod(d): {1, 2, 3, 36}; lcm_{d|6} pod(d) = pod(6) = 36; a(6) = 36/1 * 36/2 * 36/3 * 36/36 = 7776.

MATHEMATICA

pod[n_] := Times @@ Divisors[n]; a[n_] := pod[n]^Length[(d = Divisors[n])]/Times @@ (pod /@ d); Array[a, 30] (* Amiram Eldar, May 03 2020 *)

PROG

(MAGMA) [&*[ LCM([&*Divisors(d): d in Divisors(n)]) / &*Divisors(d): d in Divisors(n)]: n in [1..100]]

(PARI) pod(n) = vecprod(divisors(n));

a(n) = my(d=divisors(n), podn = pod(n)); prod(k=1, #d, podn/pod(d[k])); \\ Michel Marcus, May 03-11 2020

CROSSREFS

Cf. Similar sequences for functions lcm_{d|n} tau(d) and lcm_{d|n} sigma(d): A334470, A334471.

Cf. A000005, A000040, A007955, A266265.

Sequence in context: A128030 A239593 A214658 * A217761 A004843 A173353

Adjacent sequences:  A334486 A334487 A334488 * A334490 A334491 A334492

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, May 03 2020

STATUS

approved

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Last modified July 27 23:12 EDT 2021. Contains 346316 sequences. (Running on oeis4.)