A335070 Numbers k where records occur for phi(k)/phi(k+1), where phi is the Euler totient function (A000010).

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

Amiram Eldar, Table of n, a(n) for n = 1..75

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

Cf. A000010, A335069.

Sequence in context: A051615 A063909 A181575 * A354748 A194384 A287305

Adjacent sequences: A335067 A335068 A335069 * A335071 A335072 A335073

Keyword

nonn

Author

Amiram Eldar, May 22 2020

Status

approved