

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
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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



FORMULA



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)))


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



