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

1,2

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

Table of n, a(n) for n=1..44.

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).

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<rm, rm=r; AppendTo[a, n]], {n, 1, 10^5}]; a

Crossrefs

Cf. A000010, A001615.

Sequence in context: A152911 A317768 A362665 * A280255 A361517 A276542

Adjacent sequences: A293710 A293711 A293712 * A293714 A293715 A293716

Keyword

nonn

Author

Amiram Eldar, Oct 15 2017

Status

approved