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A062354
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sigma(n)*phi(n).
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18
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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; internal format)
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OFFSET
| 1,2
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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 (vladeta(AT)eunet.rs), Apr 17 2002
Apparently the Mobius transform of A062952. - R. J. Mathar, Oct 01 2011
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REFERENCES
| D. M. Burton, Elementary Number Theory, Allyn and Bacon Inc., Boston MA, 1976, Prob. 7.2 12, p. 141.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..10000
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FORMULA
| Multiplicative with a(p^e) = p^(e-1)*(p^(e+1)-1). - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 17 2002
Dirichlet g.f.: zeta(s)*zeta(s-2)*product_{primes p} (1-p^(1-s)-p^(-s)+p^(2-2s)). - R. J. Mathar, Oct 01 2011
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MATHEMATICA
| Table[EulerPhi[n] DivisorSigma[1, n], {n, 1, 80}] (* Carl Najafi, Aug 16 2011 *)
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PROG
| (PARI) a(n)=sigma(n)*eulerphi(n); vector(150, n, a(n))
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CROSSREFS
| Cf. A000252.
Sequence in context: A014848 A140479 A146158 * A135940 A126430 A082474
Adjacent sequences: A062351 A062352 A062353 * A062355 A062356 A062357
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KEYWORD
| easy,nonn,mult
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AUTHOR
| Jason Earls (zevi_35711(AT)yahoo.com), Jul 06 2001
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