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 A062354 a(n) = sigma(n)*phi(n). 39
 1, 3, 8, 14, 24, 24, 48, 60, 78, 72, 120, 112, 168, 144, 192, 248, 288, 234, 360, 336, 384, 360, 528, 480, 620, 504, 720, 672, 840, 576, 960, 1008, 960, 864, 1152, 1092, 1368, 1080, 1344, 1440, 1680, 1152, 1848, 1680, 1872, 1584, 2208, 1984, 2394, 1860 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Let G_n be the group of invertible 2 X 2 matrices mod n (sequence A000252). a(n) is the number of conjugacy classes in G_n. - Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Nov 13 2001 a(n) = Sum_{d|n} phi(n*d). - Vladeta Jovovic, Apr 17 2002 Apparently the Mobius transform of A062952. - R. J. Mathar, Oct 01 2011 REFERENCES D. M. Burton, Elementary Number Theory, Allyn and Bacon Inc., Boston MA, 1976, Prob. 7.2 12, p. 141. LINKS T. D. Noe, Table of n, a(n) for n=1..10000 Vaclav Kotesovec, Plot of Sum_{k=1..n} a(k) / (Pi^2 * n^3 / 18) for n = 1..1000000 J.-L. Nicolas and J. Sondow, Ramanujan, Robin, highly composite numbers, and the Riemann Hypothesis, arXiv:1211.6944 [math.HO], 2012, to appear in RAMA125 Proceedings, Contemp. Math. FORMULA Multiplicative with a(p^e) = p^(e-1)*(p^(e+1)-1). - Vladeta Jovovic, Apr 17 2002 Dirichlet g.f.: zeta(s-1)*zeta(s-2)*product_{primes p} (1-p^(1-s)-p^(-s)+p^(2-2s)). - R. J. Mathar, Oct 01 2011, corrected by Vaclav Kotesovec, Dec 17 2019 6/Pi^2 < a(n)/n^2 < 1 for n > 1. - Jonathan Sondow, Mar 06 2014 Sum_{k=1..n} a(k) ~ c * Pi^2 * n^3 / 18, where c = A330523 = Product_{primes p} (1 - 1/p^2 - 1/p^3 + 1/p^4) = 0.535896... - Vaclav Kotesovec, Dec 17 2019 Sum_{n>=1} 1/a(n) = 1.7865764... (A093827). - Amiram Eldar, Aug 20 2020 MATHEMATICA Table[EulerPhi[n] DivisorSigma[1, n], {n, 1, 80}] (* Carl Najafi, Aug 16 2011 *) PROG (PARI) a(n)=sigma(n)*eulerphi(n); vector(150, n, a(n)) CROSSREFS Cf. A000010, A000203, A000252, A062355, A064840, A093827. Sequence in context: A140479 A264689 A146158 * A257644 A135940 A126430 Adjacent sequences: A062351 A062352 A062353 * A062355 A062356 A062357 KEYWORD easy,nonn,mult AUTHOR Jason Earls, Jul 06 2001 STATUS approved

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Last modified July 22 23:31 EDT 2024. Contains 374544 sequences. (Running on oeis4.)