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A334795 a(n) = Product_{d|n} lcm(d, tau(d)) where tau(k) is the number of divisors of k (A000005).

%I A334795 #20 Sep 08 2022 08:46:25
%S A334795 1,2,6,24,10,144,14,192,54,400,22,20736,26,784,3600,15360,34,23328,38,
%T A334795 288000,7056,1936,46,3981312,750,2704,5832,790272,58,207360000,62,
%U A334795 1474560,17424,4624,19600,120932352,74,5776,24336,92160000,82,796594176,86,3066624
%N A334795 a(n) = Product_{d|n} lcm(d, tau(d)) where tau(k) is the number of divisors of k (A000005).
%C A334795 From _Robert Israel_, Jun 25 2020: (Start)
%C A334795 If p is an odd prime, a(p) = 2*p.
%C A334795 If p is a prime > 3, a(p^2) = 6*p^3.
%C A334795 If p and q are distinct odd primes, a(p*q) = 16*p^2*q^2. (End)
%H A334795 Robert Israel, <a href="/A334795/b334795.txt">Table of n, a(n) for n = 1..10000</a>
%F A334795 a(p) = 2p for p = odd primes (A065091).
%e A334795 a(6) = lcm(1, tau(1)) * lcm(2, tau(2)) * lcm(3, tau(3)) * lcm(6, tau(6)) = lcm(1, 1) * lcm(2, 2) * lcm(3, 2) * lcm(6, 4) = 1 * 2 * 6 * 12 = 144.
%p A334795 g:= d -> ilcm(d, numtheory:-tau(d)):
%p A334795 f:= n -> mul(g(d), d = numtheory:-divisors(n)):
%p A334795 map(f, [$1..100]); # _Robert Israel_, Jun 25 2020
%t A334795 a[n_] := Product[LCM[d, DivisorSigma[0, d]], {d, Divisors[n]}]; Array[a, 100] (* _Amiram Eldar_, May 12 2020 *)
%o A334795 (Magma) [&*[LCM(d, #Divisors(d)): d in Divisors(n)]: n in [1..100]]
%o A334795 (PARI) a(n) = my(d=divisors(n)); prod(k=1, #d, lcm(d[k], numdiv(d[k]))); \\ _Michel Marcus_, May 12 2020
%Y A334795 Cf. A334782 (Sum_{d|n} lcm(d, tau(d))), A334664 (Product_{d|n} gcd(d, tau(d))).
%Y A334795 Cf. A000005 (tau(n)), A009230 (lcm(n, tau(n))).
%K A334795 nonn,look
%O A334795 1,2
%A A334795 _Jaroslav Krizek_, May 12 2020