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A161785
Numbers k that are in the range of both Euler's phi function and the sigma function.
1
1, 4, 6, 8, 12, 18, 20, 24, 28, 30, 32, 36, 40, 42, 44, 48, 54, 56, 60, 72, 78, 80, 84, 96, 102, 104, 108, 110, 112, 120, 126, 128, 132, 138, 140, 144, 150, 156, 160, 162, 164, 168, 176, 180, 192, 198, 200, 204, 210, 212, 216, 222, 224, 228, 240, 252, 256, 260
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
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.
FORMULA
Intersection of A002202 and A002191.
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
Sequence in context: A090989 A161219 A310664 * A234523 A178549 A244408
KEYWORD
nonn
AUTHOR
T. D. Noe, Jun 19 2009
STATUS
approved