A307893 a(n) = lcm(sigma(n), pod(n)) / n, where sigma (k) = the sum of divisors of k (A000203) and pod(n) = the product of divisors of k (A007955).

1, 3, 4, 14, 6, 6, 8, 120, 39, 90, 12, 1008, 14, 84, 120, 1984, 18, 4212, 20, 8400, 672, 198, 24, 69120, 155, 546, 1080, 784, 30, 27000, 32, 64512, 528, 918, 1680, 25474176, 38, 570, 2184, 576000, 42, 148176, 44, 40656, 52650, 828, 48, 164560896, 399, 232500

Offset: 1

Author

Jaroslav Krizek, May 03 2019

Keywords

• nonn

Comments

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

Examples

			For n=4: a(4) = lcm(sigma(4), pod(4))/4 = lcm(7, 8)/4 = 56/4 = 14.
		

Crossrefs

Cf. A000203, A007955, A324529.

Programs

Magma

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

Mathematica

Table[LCM[DivisorSigma[1,n],Times@@Divisors[n]]/n,{n,60}] (* Harvey P. Dale, May 29 2024 *)

Formula

a(n) = A324529(n) / n.