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A029940
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a(n) = Product_{d|n} phi(d).
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11
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1, 1, 2, 2, 4, 4, 6, 8, 12, 16, 10, 32, 12, 36, 64, 64, 16, 144, 18, 256, 144, 100, 22, 1024, 80, 144, 216, 864, 28, 4096, 30, 1024, 400, 256, 576, 13824, 36, 324, 576, 16384, 40, 20736, 42, 4000, 9216, 484, 46, 131072, 252, 6400, 1024, 6912, 52, 46656, 1600
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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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If n = Product_{i} p_i^e_i then a(n) = (sqrt(n) * Product_{i} (1 - 1/p_i)^(e_i/(e_i + 1))) ^ d(n), where d(n) is the number of divisors of n (Collis, 2013). - Amiram Eldar, Jun 16 2020
a(n) = Product_{k=1..n} phi(gcd(n,k))^(1/phi(n/gcd(n,k))) = Product_{k=1..n} phi(n/gcd(n,k))^(1/phi(n/gcd(n,k))). - Richard L. Ollerton, Nov 07 2021
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MAPLE
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seq(mul(numtheory:-phi(i), i=numtheory:-divisors(n)), n=1..100); # Robert Israel, Nov 21 2014
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MATHEMATICA
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Table[Product[EulerPhi[i], {i, Divisors[n]}], {n, 100}] (* Carl Najafi, Sep 06 2011 *)
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PROG
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(PARI) a(n) = my(d = divisors(n)); prod(k=1, #d, eulerphi(d[k])); \\ Michel Marcus, Nov 21 2014
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CROSSREFS
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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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