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A079612 Largest number m such that a^n == 1 (mod m) whenever a is coprime to m. 2
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; text; internal format)
OFFSET

1,1

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. Franklin T. Adams-Watters, 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.

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.)

LINKS

Table of n, a(n) for n=1..56.

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).

CROSSREFS

Cf. A006863 (bisection except for initial term); A059379 (Jordan function).

Cf. A115000-A115003.

Cf. A143407, A143408.

Sequence in context: A171636 A270562 A100816 * A227477 A066585 A278563

Adjacent sequences:  A079609 A079610 A079611 * A079613 A079614 A079615

KEYWORD

nonn

AUTHOR

N. J. A. Sloane Jan 29 2003

EXTENSIONS

Edited by Franklin T. Adams-Watters, Dec 10 2005

Definition corrected by T. D. Noe, Aug 13 2008

Rather arbitrary term a(0) removed by Max Alekseyev, May 27 2010

STATUS

approved

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Last modified June 25 00:41 EDT 2017. Contains 288708 sequences.