A015707 Values of n where (phi(n) * sigma(n))/n is an integer and increases.

1, 6, 18, 24, 28, 40, 54, 72, 96, 117, 135, 196, 200, 216, 224, 288, 360, 384, 468, 496, 600, 640, 756, 775, 864, 891, 1000, 1080, 1152, 1372, 1488, 1521, 1568, 1701, 1792, 1944, 2016, 2160, 2176, 2480, 2592, 3100, 3159, 3200, 3375, 3456, 3744, 4320, 4455, 4608

Offset: 1

Author

Robert G. Wilson v

Keywords

• nonn

Comments

This sequence is infinite since there are infinitely many numbers m with an arbitrarily large integer value of (phi(m) * sigma(m))/m. For example, if m = 2 * 3^k, then this value is (3^(k+1)-1)/2. - Amiram Eldar, Dec 05 2018

Links

• Richard K. Guy, Divisors and desires, Amer. Math. Monthly, 104 (1997), 359-360.

Crossrefs

Cf. A015706.

Programs

Mathematica

seq = {}; rm = 0; Do[r = EulerPhi[n]*DivisorSigma[1, n]/n; If[IntegerQ[r] && r > rm, rm = r; AppendTo[seq, n]], {n, 1, 5000}]; seq (* Amiram Eldar, Dec 05 2018 *)

Extensions

Title improved by Sean A. Irvine, Dec 05 2018

a(1)=1 inserted and more terms added by Amiram Eldar, Dec 05 2018