A346574 Numbers k at which phi(tau(k))/tau(phi(k)) reaches a record high.

1, 120, 1920, 16320, 32640, 261120, 1044480, 8355840, 26732160, 67107840, 253955520, 268431360, 507911040, 2147450880, 4063288320, 9396354240

Offset

1,2

Links

Table of n, a(n) for n=1..16.

International Mathematical Olympiad, Problem N6, IMO-2020, p. 81.

Mathematica

max=0; lst={}; Do[t=EulerPhi[DivisorSigma[0, k]]/DivisorSigma[0, EulerPhi@k]; If[t>max, AppendTo[lst, k]; max=t], {k, 100000}]; lst (* Giorgos Kalogeropoulos, Jul 27 2021 *)

Prog

(PARI) lista(nn) = my(r, t); for(k=1, nn, if(r<t=eulerphi(numdiv(k))/numdiv(eulerphi(k)), r=t; print1(k, ", ")));

Crossrefs

Cf. A000005, A000010, A062821, A163109.

Sequence in context: A353200 A110839 A219720 * A244838 A266343 A293972

Adjacent sequences: A346571 A346572 A346573 * A346575 A346576 A346577

Keyword

nonn,more

Author

Jinyuan Wang, Jul 24 2021

Extensions

a(14)-a(16) from Amiram Eldar, Jul 30 2021

Status

approved