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A334731
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a(n) = Product_{d|n} gcd(sigma(d), pod(d)) where sigma(k) is the sum of divisors of k (A000203) and pod(k) is the product of divisors of k (A007955).
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3
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1, 1, 1, 1, 1, 12, 1, 1, 1, 2, 1, 48, 1, 4, 3, 1, 1, 36, 1, 4, 1, 4, 1, 576, 1, 2, 1, 224, 1, 5184, 1, 1, 3, 2, 1, 144, 1, 4, 1, 40, 1, 2304, 1, 16, 9, 4, 1, 2304, 1, 2, 9, 4, 1, 864, 1, 1792, 1, 2, 1, 995328, 1, 4, 1, 1, 1, 20736, 1, 4, 3, 128, 1, 5184, 1, 2
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OFFSET
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1,6
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LINKS
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FORMULA
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EXAMPLE
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a(6) = gcd(sigma(1), pod(1)) * gcd(sigma(2), pod(2)) * gcd(sigma(3), pod(3)) * gcd(sigma(6), pod(6)) = gcd(1, 1) * gcd(3, 2) * gcd(4, 3) * gcd(12, 36) = 1 * 1 * 1 * 12 = 12.
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MATHEMATICA
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a[n_] := Product[GCD[DivisorSigma[1, d], d^(DivisorSigma[0, d]/2)], {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) pod(n) = vecprod(divisors(n));
a(n) = my(d=divisors(n)); prod(k=1, #d, gcd(sigma(d[k]), pod(d[k]))); \\ Michel Marcus, May 09-11 2020
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CROSSREFS
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Cf. A334729 (Product_{d|n} gcd(tau(d), sigma(d))), A334663 (Sum_{d|n} gcd(sigma(d), pod(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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