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A062355
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d(n)* phi(n), where d(n) is the number of divisors function.
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6
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1, 2, 4, 6, 8, 8, 12, 16, 18, 16, 20, 24, 24, 24, 32, 40, 32, 36, 36, 48, 48, 40, 44, 64, 60, 48, 72, 72, 56, 64, 60, 96, 80, 64, 96, 108, 72, 72, 96, 128, 80, 96, 84, 120, 144, 88, 92, 160, 126, 120, 128, 144, 104, 144, 160, 192, 144, 112, 116, 192, 120, 120, 216, 224
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n)=sum of gcd(k-1,n) for 1<=k<=n and gcd(k,n)=1 (Menon's identity)
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REFERENCES
| D. M. Burton, Elementary Number Theory, Allyn and Bacon Inc., Boston MA, 1976, Prob. 7.2 12, p. 141.
P. K. Menon, On the sum gcd(a-1,n) [(a,n)=1], J. Indian Math. Soc.(N.S.), 29 (1965), 155-163.
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,1000
R. J. Mathar, Survey of Dirichlet series of multiplicative arithmetic functions, arXiv:1106.4038, Section 3.15.
M. Tarnauceanu, A generalization of the Menon's identity, arXiv:1109.2198 [math.GR]
Laszlo Toth, Menon's identity and arithmetical sums representing functions of several variables, Rend. Sem. Mat. Univ. Politec. Torino, 69 (2011), 97-110.
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FORMULA
| Dirichlet convolution of A047994 and A000010. - R. J. Mathar, Apr 15 2011
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MAPLE
| seq(tau(n)*phi(n), n=1..64); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 22 2007
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MATHEMATICA
| Table[EulerPhi[n] DivisorSigma[0, n], {n, 1, 80}] (* Carl Najafi, Aug 16 2011 *)
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PROG
| (PARI) a(n)=numdiv(n)*eulerphi(n); vector(150, n, a(n))
(PARI) { for (n=1, 1000, write("b062355.txt", n, " ", numdiv(n)*eulerphi(n)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 05 2009]
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CROSSREFS
| Cf. A062816, A079535.
Sequence in context: A107634 A060659 A063199 * A087671 A088308 A167832
Adjacent sequences: A062352 A062353 A062354 * A062356 A062357 A062358
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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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