Search: id:A079612
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%I A079612
%S A079612 0,2,24,2,240,2,504,2,480,2,264,2,65520,2,24,2,16320,2,28728,2,13200,2,
%T A079612 552,2,131040,2,24,2,6960,2,171864,2,32640,2,24,2,138181680,2,24,2,
%U A079612 1082400,2,151704,2,5520,2,1128,2,4455360,2,264,2,12720,2,86184,2,13920
%N A079612 Largest number m such that a^n = 1 (mod m) whenever a is prime to m.
%C A079612 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.
%C A079612 The numbers m with this property are the divisors of a(n) that are not 
               divisors of a(r) for r<n.
%D A079612 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.)
%F A079612 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).
%Y A079612 Cf. A006863 (bisection except for initial term); A059379 (Jordan function).
%Y A079612 Cf. A115000-A115003.
%Y A079612 Cf. A143407, A143408.
%Y A079612 Sequence in context: A118812 A054909 A100816 this_sequence A066585 A075267 
               A002743
%Y A079612 Adjacent sequences: A079609 A079610 A079611 this_sequence A079613 A079614 
               A079615
%K A079612 nonn
%O A079612 0,2
%A A079612 N. J. A. Sloane (njas(AT)research.att.com) Jan 29 2003
%E A079612 Edited by Franklin T. Adams-Watters, Dec 10 2005
%E A079612 Definition corrected by T. D. Noe (noe(AT)sspectra.com), Aug 13 2008

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