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A010554
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phi(phi(n)), where phi is Euler totient function.
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13
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| 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). [From Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 10 2010]
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REFERENCES
| 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. [From Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 10 2010]
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..10000
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].
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
S. R. Finch, Idempotents and Nilpotents Modulo n (arXiv:math.NT/0605019)
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MAPLE
| with(numtheory): f := n->phi(phi(n));
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MATHEMATICA
| Table[EulerPhi[EulerPhi[n]], {n, 0, 200}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 10 2009]
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CROSSREFS
| Cf. A000010.
Sequence in context: A077197 A117173 A103858 * A062610 A025801 A060548
Adjacent sequences: A010551 A010552 A010553 * A010555 A010556 A010557
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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