A334807 a(n) = Product_{d|n} lcm(tau(d), pod(d)) where tau(k) is the number of divisors of k (A000005) and pod(k) is the product of divisors of k (A007955).
1, 2, 6, 48, 10, 432, 14, 3072, 162, 2000, 22, 17915904, 26, 5488, 54000, 15728640, 34, 68024448, 38, 1152000000, 148176, 21296, 46, 380420285792256, 3750, 35152, 472392, 8674025472, 58, 314928000000000, 62, 1546188226560, 574992, 78608, 686000
Offset: 1
Examples
a(6) = lcm(tau(1), pod(1)) * lcm(tau(2), pod(2)) * lcm(tau(3), pod(3)) * lcm(tau(6), pod(6)) = lcm(1, 1) * lcm(2, 2) * lcm(2, 3) * lcm(4, 36) = 1 * 2 * 6 * 36 = 432.
Links
- Robert Israel, Table of n, a(n) for n = 1..5039
Crossrefs
Programs
-
Magma
[&*[LCM(#Divisors(d), &*Divisors(d)): d in Divisors(n)]: n in [1..100]];
-
Maple
pod:= proc(n) option remember; convert(numtheory:-divisors(n),`*`) end proc: f:= proc(n) local d; mul(ilcm(numtheory:-tau(d), pod(d)),d=numtheory:-divisors(n)) end proc: map(f, [$1..50]); # Robert Israel, Jan 02 2025
-
Mathematica
a[n_] := Product[LCM[DivisorSigma[0, d], Times @@ Divisors[d]], {d, Divisors[n]}]; Array[a, 35] (* Amiram Eldar, Jun 27 2020 *) -
PARI
a(n) = my(d=divisors(n)); prod(k=1, #d, lcm(numdiv(d[k]), vecprod(divisors(d[k])))); \\ Michel Marcus, Jun 27 2020
Formula
a(p) = 2p for p = odd primes (A065091).