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A079612
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Largest number m such that a^n = 1 (mod m) whenever a is prime to m.
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2
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2, 24, 2, 240, 2, 504, 2, 480, 2, 264, 2, 65520, 2, 24, 2, 16320, 2, 28728, 2, 13200, 2, 552, 2, 131040, 2, 24, 2, 6960, 2, 171864, 2, 32640, 2, 24, 2, 138181680, 2, 24, 2, 1082400, 2, 151704, 2, 5520, 2, 1128, 2, 4455360, 2, 264, 2, 12720, 2, 86184, 2, 13920
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| a(m) divides the Jordan function J_m(n) for all n except when n is a prime dividing a(m) or m=2, n=4; it is the largest number dividing all but finitely many values of J_m(n). For m > 0, a(m) also divides Sum_{k=1}^n J_m(k) for n >= the largest exceptional value. Frank Adams-Watters (FrankTAW(at)Netscape.com) Dec 10, 2005.
The numbers m with this property are the divisors of a(n) that are not divisors of a(r) for r<n.
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REFERENCES
| R. C. Vaughan and T. D. Wooley, Waring's problem: a survey, pp. 285-324 of Surveys in Number Theory (Urbana, May 21, 2000), ed. M. A. Bennett et al., Peters, 2003. (The function K(n), see p. 303.)
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FORMULA
| a(n)=2 for n odd; for n even, a(n) = product of 2^{t+2} (where 2^t exactly divides n) and p^{t+1} (where p runs through all odd primes such that p-1 divides n and p^t exactly divides n).
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CROSSREFS
| Cf. A006863 (bisection except for initial term); A059379 (Jordan function).
Cf. A115000-A115003.
Cf. A143407, A143408.
Sequence in context: A054909 A171636 A100816 * A066585 A075267 A002743
Adjacent sequences: A079609 A079610 A079611 * A079613 A079614 A079615
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com) Jan 29 2003
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EXTENSIONS
| Edited by Franklin T. Adams-Watters, Dec 10 2005
Definition corrected by T. D. Noe (noe(AT)sspectra.com), Aug 13 2008
Rather arbitrary term a(0) is removed by Max Alekseyev (maxale(AT)gmail.com), May 27 2010
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