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
KEYWORD
nonn
AUTHOR
Joseph L. Pe, Dec 13 2001
EXTENSIONS
a(17) - a(67) from Harry J. Smith, Feb 04 2010
STATUS
approved