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A247074
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a(n) = phi(n)/(Product_{primes p dividing n } gcd(p - 1, n - 1)).
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11
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1, 1, 1, 2, 1, 2, 1, 4, 3, 4, 1, 4, 1, 6, 2, 8, 1, 6, 1, 8, 3, 10, 1, 8, 5, 12, 9, 4, 1, 8, 1, 16, 5, 16, 6, 12, 1, 18, 6, 16, 1, 12, 1, 20, 3, 22, 1, 16, 7, 20, 8, 8, 1, 18, 10, 24, 9, 28, 1, 16, 1, 30, 9, 32, 3, 4, 1, 32, 11, 8, 1, 24, 1, 36, 10, 12, 15, 24, 1, 32, 27, 40, 1, 24, 4, 42, 14, 40, 1, 24, 2, 44, 15, 46
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OFFSET
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1,4
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COMMENTS
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Does every natural number appear in this sequence? If so, do they appear infinitely many times? - Eric Chen, Nov 26 2014
Number n is (Fermat) pseudoprimes (or prime) to one in a(n) of its coprime bases. That is, b^(n-1) = 1 (mod n) for one in a(n) of numbers b coprime to n. - Eric Chen, Nov 26 2014
a(p^n) = p^(n-1), where p is a prime. - Eric Chen, Nov 26 2014
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LINKS
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FORMULA
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EXAMPLE
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EulerPhi(15) = 8, and that 15 is a Fermat pseudoprime in base 1, 4, 11, and 14, the total is 4 bases, so a(15) = 8/4 = 2.
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MATHEMATICA
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a063994[n_] := Times @@ GCD[n - 1, First /@ FactorInteger@ n - 1]; a063994[1] = 1; a247074[n_] := EulerPhi[n]/a063994[n]; Array[a247074, 150]
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PROG
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(PARI) a(n)=my(f=factor(n)); eulerphi(f)/prod(i=1, #f~, gcd(f[i, 1]-1, n-1)) \\ Charles R Greathouse IV, Nov 17 2014
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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