A328272 Numbers k >= 3 where a record value of log(phi(k))/log(lambda(k)) is reached, where phi is the Euler totient function (A000010) and lambda is the Carmichael lambda function (A002322).
3, 8, 24, 7280, 13104, 21840, 32760, 65520, 2878785, 5117840, 6909084, 8636355, 19740240, 27636336, 46060560, 69090840, 138181680, 1703601900, 2271469200, 3407203800, 6814407600, 20174525280
Offset: 1
Examples
For k < 8, phi(k) = lambda(k), and log(phi(k))/log(lambda(k)) = 1. For k = 8, phi(8) = 4 and lambda(8) = 2, so log(phi(8))/log(lambda(8)) = log(4)/log(2) = 2 is a record value, and hence 8 is in this sequence.
Links
- William D. Banks, Kevin Ford, Florian Luca, Francesco Pappalardi and Igor E. Shparlinski, Values of the Euler Function in Various Sequences, Monatshefte für Mathematik, Vol. 146, No. 1 (2005), pp 1-19, alternative link.
- Lucas A. Brown, Python program.
Programs
-
Mathematica
r[n_] := Log[EulerPhi[n]]/Log[CarmichaelLambda[n]]; rm = 0; s = {}; Do[r1 = r[n]; If[r1 > rm, rm = r1; AppendTo[s, n]], {n, 3, 10^5}]; s
Extensions
a(21)-a(22) from Lucas A. Brown, Feb 28 2024
Comments