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A334664 a(n) = Product_{d|n} gcd(d, tau(d)). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..77.

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.

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 A321368

Adjacent sequences:  A334661 A334662 A334663 * A334665 A334666 A334667

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, May 07 2020

STATUS

approved

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Last modified July 27 02:39 EDT 2021. Contains 346302 sequences. (Running on oeis4.)