A307892 a(n) = lcm(tau(n), pod(n)) / n, where tau(k) = the number of divisors of k (A000005) and pod(n) = the product of divisors of k (A007955).

1, 1, 2, 6, 2, 6, 2, 8, 3, 10, 2, 144, 2, 14, 60, 320, 2, 324, 2, 1200, 84, 22, 2, 13824, 15, 26, 108, 2352, 2, 27000, 2, 3072, 132, 34, 140, 279936, 2, 38, 156, 64000, 2, 74088, 2, 5808, 4050, 46, 2, 26542080, 21, 7500, 204, 8112, 2, 157464, 220, 175616, 228

Offset: 1

Author

Jaroslav Krizek, May 03 2019

Keywords

• nonn

Comments

n divides lcm(tau(n), pod(n)) for all n >= 1.

Examples

			For n=4: a(4) = lcm(tau(4), pod(4))/4 = lcm(3, 8)/4 = 24/4 = 6.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000005, A007955, A324528.

Programs

Magma

[LCM(NumberOfDivisors(n), &*[d: d in Divisors(n)]) / n: n in [1.. 10^5]];

Mathematica

Table[(LCM[DivisorSigma[0,n],Times@@Divisors[n]])/n,{n,60}] (* Harvey P. Dale, Sep 22 2024 *)

Formula

a(n) = A324528(n) / n.