A334985 - OEIS

%I #59 Sep 08 2022 08:46:25

%S 1,6,12,168,30,18,56,960,351,450,132,6048,182,588,1800,158720,306,

%T 25272,380,84000,14112,2178,552,414720,11625,7098,29160,32928,870,

%U 405000,992,2064384,17424,15606,58800,917070336,1406,10830,85176,11520000,1722,3111696

%N a(n) = lcm(n, tau(n), sigma(n), pod(n)) / gcd(n, tau(n), sigma(n), pod(n)) where tau(k) is the number of divisors of k (A000005), sigma(k) is the sum of divisors of k (A000203) and pod(k) is the product of divisors of k (A007955).

%F a(n) = lcm(tau(n), sigma(n), pod(n)) / gcd(n, tau(n), sigma(n)).

%F a(n) = A336723(n) / A337323(n).

%e a(6) = lcm(6, tau(6), sigma(6), pod(6)) / gcd(6, tau(6), sigma(6), pod(6))  = lcm(6, 4, 12, 36) / gcd(6, 4, 12, 36) = 36 / 2 = 18.

%t a[n_] := LCM @@ {(d = DivisorSigma[0, n]), (s = DivisorSigma[1, n]), n^(d/2)} / GCD @@ {n, d, s}; Array[a, 50] (* _Amiram Eldar_, Sep 22 2020 *)

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

%o (PARI) a(n) = my(f=factor(n), v=[n, numdiv(f), sigma(f), vecprod(divisors(f))]); lcm(v)/gcd(v); \\ _Michel Marcus_, Sep 22 2020

%Y Cf. A336722, A336723, A337323.

%Y Cf. A329929 (lcm(tau(n), sigma(n), pod(n)) / gcd(tau(n), sigma(n), pod(n))).

%K nonn

%O 1,2

%A _Jaroslav Krizek_, Sep 22 2020