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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 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.)