cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A334806 a(n) = Product_{d|n} lcm(tau(d), sigma(d)) where tau(k) is the number of divisors of k (A000005) and sigma(k) is the sum of divisors of k (A000203).

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%I A334806 #10 Sep 08 2022 08:46:25
%S A334806 1,6,4,126,6,288,8,7560,156,1296,12,508032,14,1152,576,1171800,18,
%T A334806 876096,20,1143072,1024,2592,24,3657830400,558,7056,6240,4064256,30,
%U A334806 107495424,32,147646800,2304,11664,2304,1265709908736,38,7200,3136,24690355200,42
%N A334806 a(n) = Product_{d|n} lcm(tau(d), sigma(d)) where tau(k) is the number of divisors of k (A000005) and sigma(k) is the sum of divisors of k (A000203).
%F A334806 a(p) = p + 1 for p = odd primes (A065091).
%e A334806 a(6) = lcm(tau(1), sigma(1)) * lcm(tau(2), sigma(2)) * lcm(tau(3), sigma(3)) * lcm(tau(6), sigma(6)) = lcm(1, 1) * lcm(2, 3) * lcm(2, 4) * lcm(4, 12) = 1 * 6 * 4 * 12 = 288.
%t A334806 a[n_] := Product[LCM[DivisorSigma[0, d], DivisorSigma[1, d]], {d, Divisors[n]}]; Array[a, 41] (* _Amiram Eldar_, Jun 27 2020 *)
%o A334806 (Magma) [&*[LCM(#Divisors(d), &+Divisors(d)): d in Divisors(n)]: n in [1..100]]
%o A334806 (PARI) a(n) = my(d=divisors(n)); prod(k=1, #d, lcm(numdiv(d[k]), sigma(d[k]))); \\ _Michel Marcus_, Jun 27 2020
%Y A334806 Cf. A334784 (Sum_{d|n} lcm(tau(d), sigma(d))), A334729 (Product_{d|n} gcd(tau(d), sigma(d))).
%Y A334806 Cf. A000005 (tau(n)), A000203 (sigma(n)), A009278 (lcm(tau(n), sigma(n))).
%K A334806 nonn
%O A334806 1,2
%A A334806 _Jaroslav Krizek_, Jun 26 2020