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A334729
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a(n) = Product_{d|n} gcd(tau(d), sigma(d)).
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5
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1, 1, 2, 1, 2, 8, 2, 1, 2, 4, 2, 16, 2, 8, 16, 1, 2, 24, 2, 24, 16, 8, 2, 64, 2, 4, 8, 16, 2, 1024, 2, 3, 16, 4, 16, 48, 2, 8, 16, 48, 2, 2048, 2, 48, 96, 8, 2, 128, 6, 12, 16, 8, 2, 768, 16, 128, 16, 4, 2, 147456, 2, 8, 32, 3, 16, 2048, 2, 24, 16, 1024, 2
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OFFSET
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1,3
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LINKS
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FORMULA
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a(p) = 2 for p = odd primes (A065091).
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EXAMPLE
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a(6) = gcd(tau(1), sigma(1)) * gcd(tau(2), sigma(2)) * gcd(tau(3), sigma(3)) * gcd(tau(6), sigma(6)) = gcd(1, 1) * gcd(2, 3) * gcd(2, 4) * gcd(4, 12) = 1 * 1 * 2 * 4 = 8.
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MAPLE
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g:= proc(d) option remember; igcd(numtheory:-tau(d), numtheory:-sigma(d)) end proc:
f:= n -> mul(g(d), d = numtheory:-divisors(n)):
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MATHEMATICA
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a[n_] := Product[GCD[DivisorSigma[0, d], DivisorSigma[1, d]], {d, Divisors[n]}]; Array[a, 100] (* Amiram Eldar, May 09 2020 *)
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PROG
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(Magma) [&*[GCD(#Divisors(d), &+Divisors(d)): d in Divisors(n)]: n in [1..100]]
(PARI) a(n) = my(d=divisors(n)); prod(k=1, #d, gcd(numdiv(d[k]), sigma(d[k]))); \\ Michel Marcus, May 09-11 2020
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CROSSREFS
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Cf. A334491 (Product_{d|n} gcd(d, sigma(d))), A334579 (Sum_{d|n} gcd(tau(d), sigma(d))).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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