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 A174824 a(n) = period of the sequence {m^m, m >= 1} modulo n. 19
 1, 2, 6, 4, 20, 6, 42, 8, 18, 20, 110, 12, 156, 42, 60, 16, 272, 18, 342, 20, 42, 110, 506, 24, 100, 156, 54, 84, 812, 60, 930, 32, 330, 272, 420, 36, 1332, 342, 156, 40, 1640, 42, 1806, 220, 180, 506, 2162, 48, 294, 100, 816, 156, 2756, 54, 220, 168, 342 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This is a divisibility sequence: if n divides m, a(n) divides a(m). We have the equality n = a(n) for numbers n in A124240, which is related to Carmichael's function (A002322). The largest values of a(n) occur when n is prime, in which case a(n) = n*(n-1). - T. D. Noe, Feb 21 2014 LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 José María Grau and Antonio M. Oller-Marcén, On the last digit and the last non-zero digit of n^n in base b, arXiv:1203.4066 [math.NT], 2012. (See page 3) FORMULA a(n) = lcm(n, A173614(n)) = lcm(n, A002322(n)) = lcm(n, A011773(n)). If n and m are relatively prime, a(n*m) = lcm(a(n), a(m)); a(p^k) = (p-1)*p^k for p prime and k > 0. a(n) = n*A268336(n). - M. F. Hasler, Nov 13 2019 EXAMPLE For n=3, 1^1 == 1 (mod 3), 2^2 == 1 (mod 3), 3^3 == 0 (mod 3), etc. The sequence of residues 1, 1, 0, 1, 2, 0, 1, 1, 0, ... has period 6, so a(3) = 6. - Michael B. Porter, Mar 13 2018 MATHEMATICA Table[LCM[n, CarmichaelLambda[n]], {n, 100}] (* T. D. Noe, Feb 20 2014 *) PROG (PARI) a(n)=local(ps); ps=factor(n)[, 1]~; for(k=1, #ps, n=lcm(n, ps[k]-1)); n (PARI) a(n) = lcm(n, lcm(znstar(n)[2])); \\ Michel Marcus, Mar 18 2016; corrected by Michel Marcus, Nov 13 2019 (PARI) apply( {A174824(n)=lcm(lcm([p-1|p<-factor(n)[, 1]]), n)}, [1..99]) \\ [...] = znstar(n)[2], but 3x faster. - M. F. Hasler, Nov 13 2019 CROSSREFS Cf. A000312, A009262, A127699. Cf. A002322, A124240, A268336. Sequence in context: A100695 A100140 A275121 * A009262 A127699 A220769 Adjacent sequences:  A174821 A174822 A174823 * A174825 A174826 A174827 KEYWORD nonn AUTHOR Franklin T. Adams-Watters, Mar 30 2010 STATUS approved

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Last modified May 15 01:50 EDT 2021. Contains 343909 sequences. (Running on oeis4.)