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

1,2

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A000010, A000203, A062402, A067573.

Sequence in context: A182342 A178648 A241859 * A179625 A141191 A101782

Adjacent sequences: A293056 A293057 A293058 * A293060 A293061 A293062

Keyword

nonn

Author

Amiram Eldar, Oct 15 2017

Status

approved