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
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 22 2020
STATUS
approved