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A065387
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a(n) = sigma(n) + phi(n).
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43
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2, 4, 6, 9, 10, 14, 14, 19, 19, 22, 22, 32, 26, 30, 32, 39, 34, 45, 38, 50, 44, 46, 46, 68, 51, 54, 58, 68, 58, 80, 62, 79, 68, 70, 72, 103, 74, 78, 80, 106, 82, 108, 86, 104, 102, 94, 94, 140, 99, 113, 104, 122, 106, 138, 112, 144, 116, 118, 118, 184, 122, 126, 140
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OFFSET
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1,1
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COMMENTS
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a(n) = 2n for n listed in A008578, the prime numbers at the beginning of the 20th century. When a(n) = a(n + 1), n is probably listed in A066198, numbers n where phi changes as fast as sigma (the only exceptions below 10000 are 2 and 854). - Alonso del Arte, Nov 16 2005
If n is semiprime, a(n) = 2n+1+ceiling(sqrt(n))-floor(sqrt(n)). - Wesley Ivan Hurt, May 05 2015
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REFERENCES
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K. Atanassov, New integer functions, related to ψ and σ functions. IV., Bull. Number Theory Related Topics 12 (1988), pp. 31-35.
Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004. See Section B41, p. 149.
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LINKS
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A. Makowski, Aufgaben 339, Elemente der Mathematik 15 (1960), pp. 39-40.
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FORMULA
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G.f.: Sum_{k>=1} (mu(k) + 1)*x^k/(1 - x^k)^2. - Ilya Gutkovskiy, Sep 29 2017
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EXAMPLE
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a(10) = 22 because there are 4 coprimes to 10 below 10, the divisors of 10 add up to 18, and 4 + 18 = 22.
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MAPLE
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MATHEMATICA
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PROG
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(PARI) for (n=1, 1000, write("b065387.txt", n, " ", sigma(n) + eulerphi(n)) ) \\ Harry J. Smith, Oct 17 2009
(Magma) [DivisorSigma(1, k)+EulerPhi(k):k in [1..65]]; // Marius A. Burtea, Feb 09 2020
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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