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

1,2

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

Table of n, a(n) for n=1..50.

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

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 *)

Crossrefs

Cf. A015706.

Sequence in context: A275168 A236359 A011775 * A236864 A372566 A101527

Adjacent sequences: A015704 A015705 A015706 * A015708 A015709 A015710

Keyword

nonn

Author

Robert G. Wilson v

Extensions

Title improved by Sean A. Irvine, Dec 05 2018

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

Status

approved