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”).
%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