A334491 a(n) = Product_{d|n} gcd(d, sigma(d)).

1, 1, 1, 1, 1, 6, 1, 1, 1, 2, 1, 24, 1, 2, 3, 1, 1, 18, 1, 4, 1, 2, 1, 288, 1, 2, 1, 56, 1, 216, 1, 1, 3, 2, 1, 72, 1, 2, 1, 40, 1, 72, 1, 8, 9, 2, 1, 1152, 1, 2, 3, 4, 1, 108, 1, 448, 1, 2, 1, 20736, 1, 2, 1, 1, 1, 216, 1, 4, 3, 8, 1, 2592, 1, 2, 3, 8, 1, 72

Offset: 1

Author

Jaroslav Krizek, May 03 2020

Keywords

• nonn

Examples

			a(6) = gcd(1, sigma(1)) * gcd(2, sigma(2)) * gcd(3, sigma(3)) * gcd(6, sigma(6)) = gcd(1, 1) * gcd(2, 3) * gcd(3, 4) * gcd(6, 12) = 1 * 1 * 1 * 6 = 6.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A334490 (Sum_{d|n} gcd(d, sigma(d))), A007955 (pod(n) = Product_{d|n} gcd(d, pod(d))).

Cf. A000040, A000203 (sigma(n)), A009194.

Programs

Magma

[&*[GCD(d, &+Divisors(d)): d in Divisors(n)]: n in [1..100]]

Mathematica

a[n_] := Product[GCD[d, DivisorSigma[1, d]], {d, Divisors[n]}]; Array[a, 80] (* Amiram Eldar, May 03 2020 *)

PARI

a(n) = my(d=divisors(n)); prod(k=1, #d, gcd(d[k], sigma(d[k]))); \\ Michel Marcus, May 03-11 2020

Formula

a(p) = 1 for p = primes (A000040).

a(n) = Product_{d|n} A009194(d). - Antti Karttunen, May 09 2020