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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 (list; graph; refs; listen; history; text; internal format)
 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. 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 Adjacent sequences: A161782 A161783 A161784 * A161786 A161787 A161788 KEYWORD nonn AUTHOR T. D. Noe, Jun 19 2009 STATUS approved

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Last modified August 11 08:13 EDT 2024. Contains 375059 sequences. (Running on oeis4.)