A293708 Numbers n such that phi(sigma(n))/n > phi(sigma(m))/m for all m < n, where sigma is the sum of divisors function (A000203) and phi is Euler's totient function (A000010).

1, 4, 16, 36, 144, 576, 3600, 14400, 32400, 129600, 291600, 1166400, 8643600, 34574400, 77792400, 84272400, 311169600, 337089600, 700131600, 2800526400, 179233689600, 202338032400, 809352129600

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..23.

Andrzej Makowski and Andrzej Schinzel, On the functions phi(n) and sigma(n), Colloquium Mathematicae, Vol. 13, No. 1 (1964), pp. 95-99.

Mathematica

a={}; rm=0; Do[r = EulerPhi[DivisorSigma[1, 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=eulerphi(sigma(n))/n) > rmax, rmax = r; print1(n, ", ")); ); } \\ Michel Marcus, Oct 18 2017

Crossrefs

Cf. A000010, A000203, A062401.

Sequence in context: A176471 A046952 A318278 * A081456 A223403 A263385

Adjacent sequences: A293705 A293706 A293707 * A293709 A293710 A293711

Keyword

nonn,more

Author

Amiram Eldar, Oct 15 2017

Extensions

a(21)-a(23) from Robert G. Wilson v, Oct 16 2017

Status

approved