OFFSET
1,2
COMMENTS
That is, for each k there exist x and y such that k = phi(x) = sigma(y). Sigma is the sum of divisors function. Ford, Luca, and Pomerance prove that this sequence is infinite.
REFERENCES
R. K. Guy, Unsolved Problems in Number Theory, B38.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..10000
Kevin Ford, Florian Luca, and Carl Pomerance, Common values of the arithmetic functions phi and sigma, Bull. London Math. Soc. 42 (2010), pp. 478-488.
MATHEMATICA
Intersection[EulerPhi[Range[9660]], DivisorSigma[1, Range[2112]]]
PROG
(PARI) list(lim)={
my(u=vector(lim\=1, k, sigma(k)), v=vector(if(lim>63, 3*lim*log(log(lim))\1, 210), k, eulerphi(k)));
select(n->n<=lim, setintersect(vecsort(v, , 8), vecsort(u, , 8)))
}; \\ Charles R Greathouse IV, Feb 05 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
T. D. Noe, Jun 19 2009
STATUS
approved