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A337323
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a(n) = gcd(n, tau(n), sigma(n), pod(n)) where tau(k) is the number of divisors of k (A000005), 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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5
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1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 3, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 8, 1, 2, 1, 12, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 1
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OFFSET
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1,6
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COMMENTS
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GCD(n, tau(n), sigma(n), pod(n)) = GCD(n, tau(n), sigma(n)). - David A. Corneth, Aug 24 2020
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LINKS
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FORMULA
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EXAMPLE
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a(6) = gcd(6, tau(6), sigma(6), pod(6)) = gcd(6, 4, 12, 36) = 2.
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MAPLE
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f:= proc(n) uses numtheory; igcd(n, tau(n), sigma(n)) end proc:
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MATHEMATICA
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a[n_] := GCD @@ {n, DivisorSigma[0, n], DivisorSigma[1, n]}; Array[a, 100] (* Amiram Eldar, Aug 24 2020 *)
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PROG
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(Magma) [GCD([n, #Divisors(n), &+Divisors(n), &*Divisors(n)]): n in [1..100]]
(PARI) a(n) = my(f=factor(n)); gcd([n, sigma(f), numdiv(f)]); \\ Michel Marcus, Apr 01 2021
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CROSSREFS
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Cf. A336722 (gcd(tau(n), sigma(n), pod(n))).
Cf. A337324 (least m such that gcd(m, tau(m), sigma(m), pod(m)) = n).
Cf. A336723 (lcm(tau(n), sigma(n), pod(n))) = (lcm(n, tau(n), sigma(n), pod(n))).
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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