A293059 Numbers k such that sigma(phi(k))/k > sigma(phi(m))/m for all m < k, where sigma is the sum of divisors function (A000203) and phi is Euler's totient function (A000010).

1, 5, 7, 13, 31, 37, 61, 181, 241, 421, 899, 1321, 1333, 1763, 2161, 2521, 5183, 7561, 12601, 15121, 28187, 30241, 55441, 110881, 167137, 278263, 332641, 555911, 666917, 722473, 1443853, 2165407, 3607403, 4324321, 7212581, 8654539, 10817761, 21631147, 36768847

Offset: 1

Author

Amiram Eldar, Oct 15 2017

Keywords

• nonn

Comments

Alaoglu and Erdős proved that lim sup sigma(phi(n))/n = oo, thus this sequence is infinite.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..55
• Leon Alaoglu and Paul Erdős, A conjecture in elementary number theory, Bulletin of the American Mathematical Society, Vol. 50, No. 12 (1944), pp. 881-882.
• Florian Luca and Carl Pomerance, On some problems of Makowski-Schinzel and Erdős concerning the arithmetical functions phi and sigma, Colloquium Mathematicae, Vol. 92, No. 1 (2002), pp. 111-130.

Crossrefs

Cf. A000010, A000203, A062402, A067573.

Programs

Mathematica

a={}; rm=0; Do[r = DivisorSigma[1, EulerPhi[n]]/n; If[r>rm, rm=r; AppendTo[a,n]],{n,1,100000}]; a

PARI

lista(nn) = {my(rmax = 0); for (n=1, nn, if ((r=sigma(eulerphi(n))/n) > rmax, rmax = r; print1(n, ", ")););} \\ Michel Marcus, Oct 18 2017