A293713 Numbers n such that phi(psi(n))/n < phi(psi(m))/m for all m < n, where phi is Euler's totient function (A000010) and psi is the Dedekind psi function (A001615).

1, 3, 4, 5, 11, 17, 23, 25, 29, 59, 89, 149, 179, 239, 269, 359, 377, 389, 419, 839, 1049, 1259, 1889, 2099, 2309, 9239, 11549, 13859, 20789, 23099, 25409, 30029, 90089, 180179, 210209, 270269, 300299, 330329, 390389, 420419, 540539, 570569, 1017917, 1018013

Offset: 1

Author

Amiram Eldar, Oct 15 2017

Keywords

• nonn

Comments

Sândor proved that lim inf phi(psi(n))/n = 0, hence this sequence is infinite.

References

• Jôzsef Sândor, On Dedekind’s arithmetical function, Seminarul de Teoria Structurilor, Univ. Timisoara, No. 51, 1988, pp. 1-15.

Links

• Jôzsef Sândor, On the composition of some arithmetic functions, II, Journal of Inequalities in Pure and Applied Mathematics, Vol. 6, Issue 3, Article 73 (2005).

Crossrefs

Cf. A000010, A001615.

Programs

Mathematica

psi[n_] := If[n < 1, 0, n*Sum[MoebiusMu[d]^2/d, {d, Divisors@n}]]; a={}; rm=2; Do[r=EulerPhi[psi[n]]/n; If[r