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 A079612 Largest number m such that a^n == 1 (mod m) whenever a is coprime to m. 10
 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 1, a(n) = 2*A075180(n-1). (End) We have 2*A075180(2n-1) = A006863(n) by definition, and A006863(n) = a(2n) by the comments in A006863. Hence a(n) = 2*A075180(n-1) for all even n. For all odd n > 1, we have a(n) = 2, which is also equal to 2*A075180(n-1). So the formula above is true. - Jianing Song, Apr 05 2021 PROG (PARI) a(n) = {if (n%2, 2, res = 1; forprime(p=2, n+1, if (!(n % (p-1)), t = valuation(n, p); if (p==2, if (t, res *= p^(t+2)), res *= p^(t+1)); ); ); res; ); } \\ Michel Marcus, May 12 2018 CROSSREFS Cf. A006863 (bisection except for initial term); A059379 (Jordan function). Cf. A075180, A115000, A115001, A115002, A115003. Cf. A143407, A143408, A185633, A322315. Sequence in context: A350257 A270562 A100816 * A329263 A227477 A351850 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 September 28 02:47 EDT 2022. Contains 357063 sequences. (Running on oeis4.)