A334471 - OEIS

%I #18 Sep 08 2022 08:46:25

%S 1,3,4,441,6,144,8,385875,2704,324,12,12446784,14,576,576,

%T 37418184916875,18,197413632,20,42007896,1024,1296,24,38118276000000,

%U 34596,1764,35152000,99574272,30,26873856,32,1409355934894096875,2304,2916,2304,1695648500686393344

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

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

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

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

%e 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.

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

%o (Magma) [&*[ LCM([&+Divisors(d): d in Divisors(n)]) / &+Divisors(d): d in Divisors(n)]: n in [1..100]]

%o (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

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

%Y Cf. A000005, A000040, A069934, A206032.

%K nonn

%O 1,2

%A _Jaroslav Krizek_, May 01 2020