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

1,2

Links

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

Formula

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

Example

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.

Mathematica

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

Prog

(Magma) [&*[GCD(d, #Divisors(d)): d in Divisors(n)]: n in [1..100]]
(PARI) a(n) = my(d=divisors(n)); prod(k=1, #d, gcd(d[k], numdiv(d[k]))); \\ Michel Marcus, May 08-11 2020

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))).

Sequence in context: A055684 A300584 A024559 * A061797 A068341 A360738

Adjacent sequences: A334661 A334662 A334663 * A334665 A334666 A334667

Keyword

nonn

Author

Jaroslav Krizek, May 07 2020

Status

approved