A329929 a(n) = lcm(tau(n), sigma(n), pod(n)) / gcd(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, 6, 12, 168, 30, 9, 56, 960, 351, 450, 132, 6048, 182, 294, 1800, 158720, 306, 25272, 380, 84000, 14112, 1089, 552, 414720, 11625, 7098, 29160, 32928, 870, 101250, 992, 2064384, 17424, 15606, 58800, 917070336, 1406, 5415, 85176, 11520000, 1722, 777924, 1892
Offset: 1
Keywords
Examples
a(6) = lcm(tau(6), sigma(6), pod(6)) / gcd(tau(6), sigma(6), pod(6)) = lcm(4, 12, 36) / gcd(4, 12, 36) = 36 / 4 = 9.
Crossrefs
Programs
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Magma
[LCM([#Divisors(n), &+Divisors(n), &*Divisors(n)]) / GCD([#Divisors(n), &+Divisors(n), &*Divisors(n)]): n in [1..100]];
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Mathematica
a[n_] := LCM @@ (t = {(d = DivisorSigma[0, n]), n^(d/2), DivisorSigma[1, n]}) / GCD @@ t; Array[a, 50] (* Amiram Eldar, Aug 31 2020 *) -
PARI
a(n) = my(f=factor(n), v=[numdiv(f), sigma(f), vecprod(divisors(f))]); lcm(v)/gcd(v); \\ Michel Marcus, Aug 31 2020
Comments