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

Author

Jinyuan Wang, Jul 24 2021

Keywords

• nonn
• more

Links

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

Crossrefs

Cf. A000005, A000010, A062821, A163109.

Programs

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 *)

PARI

lista(nn) = my(r, t); for(k=1, nn, if(r
				

Extensions

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