A334807 a(n) = Product_{d|n} lcm(tau(d), pod(d)) where tau(k) is the number of divisors of k (A000005) and pod(k) is the product of divisors of k (A007955).

1, 2, 6, 48, 10, 432, 14, 3072, 162, 2000, 22, 17915904, 26, 5488, 54000, 15728640, 34, 68024448, 38, 1152000000, 148176, 21296, 46, 380420285792256, 3750, 35152, 472392, 8674025472, 58, 314928000000000, 62, 1546188226560, 574992, 78608, 686000

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..5039

Formula

a(p) = 2p for p = odd primes (A065091).

Example

a(6) = lcm(tau(1), pod(1)) * lcm(tau(2), pod(2)) * lcm(tau(3), pod(3)) * lcm(tau(6), pod(6)) = lcm(1, 1) * lcm(2, 2) * lcm(2, 3) * lcm(4, 36) = 1 * 2 * 6 * 36 = 432.

Maple

pod:= proc(n) option remember; convert(numtheory:-divisors(n), `*`) end proc:
f:= proc(n) local d; mul(ilcm(numtheory:-tau(d), pod(d)), d=numtheory:-divisors(n)) end proc:
map(f, [$1..50]); # Robert Israel, Jan 02 2025

Mathematica

a[n_] := Product[LCM[DivisorSigma[0, d], Times @@ Divisors[d]], {d, Divisors[n]}]; Array[a, 35] (* Amiram Eldar, Jun 27 2020 *)

Prog

(Magma) [&*[LCM(#Divisors(d), &*Divisors(d)): d in Divisors(n)]: n in [1..100]];
(PARI) a(n) = my(d=divisors(n)); prod(k=1, #d, lcm(numdiv(d[k]), vecprod(divisors(d[k])))); \\ Michel Marcus, Jun 27 2020

Crossrefs

Cf. A334793 (Sum_{d|n} lcm(tau(d), pod(d))), A334730 (Product_{d|n} gcd(tau(d), pod(d))).

Cf. A000005 (tau(n)), A007955 (pod(n)), A324528 (lcm(tau(n), pod(n))).

Sequence in context: A145502 A274702 A072444 * A052596 A344676 A098710

Adjacent sequences: A334804 A334805 A334806 * A334808 A334809 A334810

Keyword

nonn,look

Author

Jaroslav Krizek, Jun 26 2020

Status

approved