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A065395
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Commutator of sigma and phi functions.
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13
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0, -1, 1, -3, 5, -1, 8, -1, 0, 1, 14, -5, 22, 4, 7, -15, 25, -12, 31, 3, 12, 6, 28, -1, 12, 16, 23, 4, 48, -9, 56, -5, 26, 13, 44, -44, 73, 23, 36, 7, 78, -4, 76, 18, 36, 12, 56, -29, 60, -18, 39, 18, 80, 7, 66, 28, 59, 32, 74, -17, 138, 40, 43, -63, 100, -6
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OFFSET
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1,4
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COMMENTS
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Golomb (1993) proved that the terms are both positive and negative infinitely often. - Amiram Eldar, Feb 27 2024
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REFERENCES
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Solomon W. Golomb, Equality among number-theoretic functions, Abstracts Amer. Math. Soc., Vol. 14 (1993), pp. 415-416.
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LINKS
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FORMULA
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EXAMPLE
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n = 13: sigma(13) = 14, phi(14) = 6, phi(13) = 12, sigma(12) = 28, a(13) = 28-6 = 22.
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MAPLE
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MATHEMATICA
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Table[DivisorSigma[1, EulerPhi[n]] - EulerPhi[DivisorSigma[1, n]], {n, 100}] (* T. D. Noe, Nov 04 2013 *)
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PROG
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(PARI) { for (n=1, 1000, a=sigma(eulerphi(n)) - eulerphi(sigma(n)); write("b065395.txt", n, " ", a) ) } \\ Harry J. Smith, Oct 18 2009
(Magma) [DivisorSigma(1, EulerPhi(n))-EulerPhi(DivisorSigma(1, n)): n in [1..70]]; // Bruno Berselli, Oct 20 2015
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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