A334471
a(n) = Product_{d|n} (A069934(n) / sigma(d)) where A069934(n) = lcm_{d|n} sigma(d).
Original entry on oeis.org
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
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.
Cf. Similar sequence with tau(d):
A334470.
-
[&*[ LCM([&+Divisors(d): d in Divisors(n)]) / &+Divisors(d): d in Divisors(n)]: n in [1..100]]
-
a[n_] := (LCM @@ (s = DivisorSigma[1, Divisors[n]]))^Length[s] / Times @@ s; Array[a, 36] (* Amiram Eldar, May 02 2020 *)
-
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
A334489
a(n) = Product_{d|n} (pod(n)/pod(d)) where pod(n) = A007955(n), the product of divisors of n.
Original entry on oeis.org
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
Offset: 1
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.
Cf. Similar sequences for functions lcm_{d|n} tau(d) and lcm_{d|n} sigma(d):
A334470,
A334471.
-
[&*[ LCM([&*Divisors(d): d in Divisors(n)]) / &*Divisors(d): d in Divisors(n)]: n in [1..100]]
-
pod[n_] := Times @@ Divisors[n]; a[n_] := pod[n]^Length[(d = Divisors[n])]/Times @@ (pod /@ d); Array[a, 30] (* Amiram Eldar, May 03 2020 *)
-
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
Showing 1-2 of 2 results.