login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

a(n) = Product_{d|n} (A069934(n) / sigma(d)) where A069934(n) = lcm_{d|n} sigma(d).
2

%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