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 A334985 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). 1
 1, 6, 12, 168, 30, 18, 56, 960, 351, 450, 132, 6048, 182, 588, 1800, 158720, 306, 25272, 380, 84000, 14112, 2178, 552, 414720, 11625, 7098, 29160, 32928, 870, 405000, 992, 2064384, 17424, 15606, 58800, 917070336, 1406, 10830, 85176, 11520000, 1722, 3111696 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..42. FORMULA a(n) = lcm(tau(n), sigma(n), pod(n)) / gcd(n, tau(n), sigma(n)). a(n) = A336723(n) / A337323(n). EXAMPLE 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. MATHEMATICA 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 *) PROG (Magma) [LCM([#Divisors(n), &+Divisors(n), &*Divisors(n)]) / GCD([#Divisors(n), &+Divisors(n), &*Divisors(n)]): n in [1..100]] (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 CROSSREFS Cf. A336722, A336723, A337323. Cf. A329929 (lcm(tau(n), sigma(n), pod(n)) / gcd(tau(n), sigma(n), pod(n))). Sequence in context: A002922 A334916 A329929 * A336723 A334805 A324980 Adjacent sequences: A334982 A334983 A334984 * A334986 A334987 A334988 KEYWORD nonn AUTHOR Jaroslav Krizek, Sep 22 2020 STATUS approved

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Last modified August 4 17:28 EDT 2024. Contains 374923 sequences. (Running on oeis4.)