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A336722
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a(n) = gcd(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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7
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1, 1, 1, 1, 1, 4, 1, 1, 1, 2, 1, 2, 1, 4, 1, 1, 1, 3, 1, 2, 1, 4, 1, 4, 1, 2, 1, 2, 1, 8, 1, 1, 1, 2, 1, 1, 1, 4, 1, 2, 1, 8, 1, 2, 3, 4, 1, 2, 1, 1, 1, 2, 1, 8, 1, 8, 1, 2, 1, 12, 1, 4, 1, 1, 1, 8, 1, 2, 1, 8, 1, 3, 1, 2, 1, 2, 1, 8, 1, 2, 1, 2, 1, 4, 1, 4, 1, 4, 1, 6, 1, 2, 1, 4, 1, 12, 1, 1, 3, 1, 1, 8, 1, 2, 1
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OFFSET
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1,6
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COMMENTS
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a(n) = tau(n) for numbers n: 1, 6, 14, 22, 30, 38, 42, 46, 54, 56, 60, 62, 66, 70, 78, 86, 94, 96, 102, ...
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LINKS
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FORMULA
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EXAMPLE
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a(6) = gcd(tau(6), sigma(6), pod(6)) = gcd(4, 12, 36) = 4.
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MATHEMATICA
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a[n_] := GCD @@ {(d = DivisorSigma[0, n]), DivisorSigma[1, n], n^(d/2)}; Array[a, 100] (* Amiram Eldar, Aug 01 2020 *)
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PROG
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(Magma) [GCD([#Divisors(n), &+Divisors(n), &*Divisors(n)]): n in [1..100]]
(PARI)
A007955(n) = if(issquare(n, &n), n^numdiv(n^2), n^(numdiv(n)/2)); \\ From A007955
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CROSSREFS
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Cf. A277521 (numbers k such that a(k) = tau(k) and simultaneously A336723(k) = pod(k)).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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