A066168 a(n) = least k such that phi(k) > sigma(n).

3, 5, 7, 11, 11, 17, 11, 17, 17, 23, 17, 31, 17, 29, 29, 37, 23, 41, 23, 47, 37, 41, 29, 67, 37, 47, 43, 59, 37, 79, 37, 67, 53, 59, 53, 97, 41, 67, 59, 97, 47, 101, 47, 89, 83, 79, 53, 127, 59, 97, 79, 101, 59, 127, 79, 127, 83, 97, 67, 173, 67, 101, 107, 131, 89, 149, 71

Offset

1,1

Comments

Sigma dominates phi. Heuristically, a(n) = first time when phi(n) overtakes sigma(n), if n is thought of as time. a(n) - n can be thought of as the "lag at time n" of phi behind sigma.

It is easily shown that all terms a(n) are primes.

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Example

a(3) = 7 since phi(7) = 6 > sigma(3) = 4 and 7 is the first number to satisfy the inequality.

Mathematica

With[{ep=EulerPhi[Range[200]]}, Table[Position[ep, _?(#>DivisorSigma[1, m]&), {1}, 1], {m, 70}]]//Flatten (* Harvey P. Dale, May 03 2016 *)

Prog

(PARI) { for (n=1, 1000, s=sigma(n); k=1; while (eulerphi(k) <= s, k++); write("b066168.txt", n, " ", k) ) } \\ Harry J. Smith, Feb 04 2010

Crossrefs

Sequence in context: A208643 A123252 A352185 * A058024 A215464 A260910

Adjacent sequences: A066165 A066166 A066167 * A066169 A066170 A066171

Keyword

nonn

Author

Joseph L. Pe, Dec 13 2001

Extensions

a(17) - a(67) from Harry J. Smith, Feb 04 2010

Status

approved