A335069 Numbers k where records occur for phi(k+1)/phi(k), where phi is the Euler totient function (A000010).

1, 2, 6, 30, 210, 2310, 30030, 120120, 690690, 1021020, 2042040, 4084080, 9699690, 58198140, 96996900, 106696590, 223092870, 892371480, 6469693230, 6915878970, 19409079690, 32348466150, 71166625530, 200560490130, 7420738134810, 8624101075590

Offset

1,2

Comments

Somayajulu (1950) proved that phi(k+1)/phi(k) is unbounded, hence this sequence is infinite.

a(27) <= 16445960190660. - Giovanni Resta, May 24 2020

References

József Sándor, Dragoslav S. Mitrinovic, Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, page 16.

Links

Table of n, a(n) for n=1..26.

B. S. K. R. Somayajulu, On Euler's totient function phi(n), Math. Student, Vol. 18 (1950), pp. 31-32; entire issues 1 and 2.

Example

The values of phi(k+1)/phi(k) for the first terms are 1, 2, 3, 3.75, 4.375, 4.8125, ...

Mathematica

rm = 0; s1 = 1; seq = {}; Do[s2 = EulerPhi[n]; If[(r = s2/s1) > rm, rm = r; AppendTo[seq, n-1]]; s1 = s2, {n, 2, 10^6}]; seq

Crossrefs

Cf. A000010, A335070.

Sequence in context: A096775 A331665 A171989 * A361807 A233438 A002110

Adjacent sequences: A335066 A335067 A335068 * A335070 A335071 A335072

Keyword

nonn,more

Author

Amiram Eldar, May 22 2020

Extensions

a(24)-a(26) from Giovanni Resta, May 24 2020

Status

approved