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A010554
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a(n) = phi(phi(n)), where phi is the Euler totient function.
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38
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1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 4, 2, 4, 2, 4, 4, 8, 2, 6, 4, 4, 4, 10, 4, 8, 4, 6, 4, 12, 4, 8, 8, 8, 8, 8, 4, 12, 6, 8, 8, 16, 4, 12, 8, 8, 10, 22, 8, 12, 8, 16, 8, 24, 6, 16, 8, 12, 12, 28, 8, 16, 8, 12, 16, 16, 8, 20, 16, 20, 8, 24, 8
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OFFSET
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1,5
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COMMENTS
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If n has a primitive root, then it has exactly phi(phi(n)) of them (Burton 1989, p. 188), which means that if p is a prime number, then there are exactly phi(p-1) incongruent primitive roots of p (Burton 1989). - Jonathan Vos Post, Sep 10 2010
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 840.
Burton, D. M. "The Order of an Integer Modulo n," "Primitive Roots for Primes," and "Composite Numbers Having Primitive Roots." Sections 8.1-8.3 in Elementary Number Theory, 4th ed. Dubuque, IA: William C. Brown Publishers, pp. 184-205, 1989.
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LINKS
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
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MAPLE
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with(numtheory): f := n->phi(phi(n));
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MATHEMATICA
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PROG
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(Haskell)
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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STATUS
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approved
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