OFFSET
1,4
COMMENTS
Golomb (1993) proved that the terms are both positive and negative infinitely often. - Amiram Eldar, Feb 27 2024
REFERENCES
Solomon W. Golomb, Equality among number-theoretic functions, Abstracts Amer. Math. Soc., Vol. 14 (1993), pp. 415-416.
LINKS
Harry J. Smith, Table of n, a(n) for n = 1..1000
Jean-Marie De Koninck and Florian Luca, On the composition of the Euler function and the sum of divisors function, Colloquium Mathematicum, Vol. 108, No. 1 (2007), pp. 31-51.
Solomon W. Golomb, Equality among number-theoretic functions, Unpublished manuscript. (Annotated scanned copy)
FORMULA
EXAMPLE
n = 13: sigma(13) = 14, phi(14) = 6, phi(13) = 12, sigma(12) = 28, a(13) = 28-6 = 22.
MAPLE
with(numtheory); A065395:=n->sigma(phi(n))-phi(sigma(n)); seq(A065395(n), n=1..100); # Wesley Ivan Hurt, Dec 26 2013
MATHEMATICA
Table[DivisorSigma[1, EulerPhi[n]] - EulerPhi[DivisorSigma[1, n]], {n, 100}] (* T. D. Noe, Nov 04 2013 *)
PROG
(PARI) a(n) = { sigma(eulerphi(n)) - eulerphi(sigma(n)) } \\ Harry J. Smith, Oct 18 2009
(Magma) [DivisorSigma(1, EulerPhi(n))-EulerPhi(DivisorSigma(1, n)): n in [1..70]]; // Bruno Berselli, Oct 20 2015
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Labos Elemer, Nov 05 2001
STATUS
approved