A293712 Numbers n such that psi(phi(n))/n > psi(phi(m))/m for all m < n, where phi is Euler's totient function (A000010) and psi is the Dedekind psi function (A001615).

1, 5, 7, 13, 19, 31, 61, 151, 181, 211, 421, 631, 1051, 1471, 2311, 4621, 9241, 11551, 18481, 25411, 32341, 34651, 43891, 60653, 120121, 150151, 180181, 270271, 300301, 330331, 390391, 420421, 450451, 540541, 600601, 660661, 840841, 870871, 1023053, 2045003

Offset

1,2

Comments

Sândor proved that lim sup psi(phi(n))/n = oo, 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..40.

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

Crossrefs

Cf. A000010, A001615.

Sequence in context: A006512 A074304 A264865 * A297674 A072677 A117249

Adjacent sequences: A293709 A293710 A293711 * A293713 A293714 A293715

Keyword

nonn

Author

Amiram Eldar, Oct 15 2017

Status

approved