A334664 a(n) = Product_{d|n} gcd(d, tau(d)).

1, 2, 1, 2, 1, 4, 1, 8, 3, 4, 1, 24, 1, 4, 1, 8, 1, 72, 1, 8, 1, 4, 1, 768, 1, 4, 3, 8, 1, 16, 1, 16, 1, 4, 1, 3888, 1, 4, 1, 256, 1, 16, 1, 8, 9, 4, 1, 1536, 1, 8, 1, 8, 1, 144, 1, 256, 1, 4, 1, 2304, 1, 4, 9, 16, 1, 16, 1, 8, 1, 16, 1, 1492992, 1, 4, 3, 8, 1

Offset: 1

Author

Jaroslav Krizek, May 07 2020

Keywords

• nonn

Examples

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

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A322979 (Sum_{d|n} gcd(d, tau(d))), A334491 (Product_{d|n} gcd(d, sigma(d))).

Cf. A000005 (tau(n)), A000203 (sigma(n)), A009191 (gcd(n, tau(n))).

Programs

Magma

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

Mathematica

Table[Times@@GCD[Divisors[n],DivisorSigma[0,Divisors[n]]],{n,80}] (* Harvey P. Dale, Mar 30 2024 *)

PARI

a(n) = my(d=divisors(n)); prod(k=1, #d, gcd(d[k], numdiv(d[k]))); \\ Michel Marcus, May 08-11 2020

Formula

a(p) = 1 for p = odd primes (A065091).