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A335070
Numbers k where records occur for phi(k)/phi(k+1), where phi is the Euler totient function (A000010).
2
1, 5, 11, 17, 23, 29, 59, 89, 149, 179, 209, 389, 419, 839, 1049, 1259, 1889, 2099, 2309, 9239, 11549, 13859, 20789, 23099, 25409, 30029, 90089, 180179, 210209, 270269, 300299, 330329, 390389, 420419, 510509, 570569, 1021019, 2042039, 3063059, 4084079, 4594589
OFFSET
1,2
COMMENTS
Somayajulu (1950) proved that phi(k+1)/phi(k) can be arbitrarily close to 0, therefore phi(k)/phi(k+1) is unbounded and this sequence is infinite.
REFERENCES
József Sándor, Dragoslav S. Mitrinovic, Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, page 16.
B. S. K. R. Somayajulu, On Euler's totient function phi(n), Math. Student, Vol. 18 (1950), pp. 31-32.
LINKS
EXAMPLE
The values of phi(k)/phi(k+1) for the first terms are 1, 2, 2.5, 2.666..., 2.75, 3.5, ...
MATHEMATICA
rm = 0; s1 = 1; seq = {}; Do[s2 = EulerPhi[n]; If[(r = s1/s2) > rm, rm = r; AppendTo[seq, n-1]]; s1 = s2, {n, 2, 10^6}]; seq
CROSSREFS
Sequence in context: A051615 A063909 A181575 * A354748 A194384 A287305
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 22 2020
STATUS
approved