A334807 - OEIS

%I #10 Sep 08 2022 08:46:25

%S 1,2,6,48,10,432,14,3072,162,2000,22,17915904,26,5488,54000,15728640,

%T 34,68024448,38,1152000000,148176,21296,46,380420285792256,3750,35152,

%U 472392,8674025472,58,314928000000000,62,1546188226560,574992,78608,686000

%N 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).

%F a(p) = 2p for p = odd primes (A065091).

%e 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.

%t a[n_] := Product[LCM[DivisorSigma[0, d], Times @@ Divisors[d]], {d, Divisors[n]}]; Array[a, 35] (* _Amiram Eldar_, Jun 27 2020 *)

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

%o (PARI) a(n) = my(d=divisors(n)); prod(k=1, #d, lcm(numdiv(d[k]), vecprod(divisors(d[k])))); \\ _Michel Marcus_, Jun 27 2020

%Y Cf. A334793 (Sum_{d|n} lcm(tau(d), pod(d))), A334730 (Product_{d|n} gcd(tau(d), pod(d))).

%Y Cf. A000005 (tau(n)), A007955 (pod(n)), A324528 (lcm(tau(n), pod(n))).

%K nonn

%O 1,2

%A _Jaroslav Krizek_, Jun 26 2020