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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).

%I A334807 #16 Jan 02 2025 20:04:36
%S A334807 1,2,6,48,10,432,14,3072,162,2000,22,17915904,26,5488,54000,15728640,
%T A334807 34,68024448,38,1152000000,148176,21296,46,380420285792256,3750,35152,
%U A334807 472392,8674025472,58,314928000000000,62,1546188226560,574992,78608,686000
%N 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).
%H A334807 Robert Israel, <a href="/A334807/b334807.txt">Table of n, a(n) for n = 1..5039</a>
%F A334807 a(p) = 2p for p = odd primes (A065091).
%e A334807 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.
%p A334807 pod:= proc(n) option remember; convert(numtheory:-divisors(n),`*`) end proc:
%p A334807 f:= proc(n) local d; mul(ilcm(numtheory:-tau(d), pod(d)),d=numtheory:-divisors(n)) end proc:
%p A334807 map(f, [$1..50]); # _Robert Israel_, Jan 02 2025
%t A334807 a[n_] := Product[LCM[DivisorSigma[0, d], Times @@ Divisors[d]], {d, Divisors[n]}]; Array[a, 35] (* _Amiram Eldar_, Jun 27 2020 *)
%o A334807 (Magma) [&*[LCM(#Divisors(d), &*Divisors(d)): d in Divisors(n)]: n in [1..100]];
%o A334807 (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 A334807 Cf. A334793 (Sum_{d|n} lcm(tau(d), pod(d))), A334730 (Product_{d|n} gcd(tau(d), pod(d))).
%Y A334807 Cf. A000005 (tau(n)), A007955 (pod(n)), A324528 (lcm(tau(n), pod(n))).
%K A334807 nonn,look
%O A334807 1,2
%A A334807 _Jaroslav Krizek_, Jun 26 2020