A334471 a(n) = Product_{d|n} (A069934(n) / sigma(d)) where A069934(n) = lcm_{d|n} sigma(d).

1, 3, 4, 441, 6, 144, 8, 385875, 2704, 324, 12, 12446784, 14, 576, 576, 37418184916875, 18, 197413632, 20, 42007896, 1024, 1296, 24, 38118276000000, 34596, 1764, 35152000, 99574272, 30, 26873856, 32, 1409355934894096875, 2304, 2916, 2304, 1695648500686393344

Offset

1,2

Links

Table of n, a(n) for n=1..36.

Formula

a(n) = ((lcm_{d|n} sigma(d))^tau(n)) / Product_{d|n} (sigma(d)).

a(n) = A069934(n)^A000005(n) / A206032(n).

a(p) = p + 1 for p = primes (A000040).

Example

For n = 6; divisors d of 6: {1, 2, 3, 6}; sigma(d): {1, 3, 4, 12}; lcm_{d|6} sigma(d) = 12; a(6) = 12/1 * 12/3 * 12/4 * 12/12 = 144.

Mathematica

a[n_] := (LCM @@ (s = DivisorSigma[1, Divisors[n]]))^Length[s] / Times @@ s; Array[a, 36] (* Amiram Eldar, May 02 2020 *)

Prog

(Magma) [&*[ LCM([&+Divisors(d): d in Divisors(n)]) / &+Divisors(d): d in Divisors(n)]: n in [1..100]]
(PARI) a(n) = {my(d=divisors(n), lcms = lcm(vector(#d, k, sigma(d[k])))); vecprod(vector(#d, k, lcms/sigma(d[k]))); } \\ Michel Marcus, May 02 2020

Crossrefs

Cf. Similar sequence with tau(d): A334470.

Cf. A000005, A000040, A069934, A206032.

Sequence in context: A069970 A305169 A316759 * A153063 A165499 A094396

Adjacent sequences: A334468 A334469 A334470 * A334472 A334473 A334474

Keyword

nonn

Author

Jaroslav Krizek, May 01 2020

Status

approved