cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A062516 Numbers k such that 2*tau(k) = phi(k).

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%I A062516 #17 Jun 28 2022 18:26:21
%S A062516 5,9,15,28,40,72,84,90,120
%N A062516 Numbers k such that 2*tau(k) = phi(k).
%C A062516 Sequence is finite, since for large k and suitable constants and epsilon: phi(k) - 2*tau(k) > c1*k^(2/3) - 4*c2*k^(1/2) > 0 if k > c3, so phi(k) - 2*tau(k) > 0, QED. Moreover, phi(k) = m*tau(k) has at most finitely many solutions for any constant m or even for slowly increasing functions like m(k) = k^(epsilon). - _Labos Elemer_, Jul 20 2001
%t A062516 Select[Range[150],2*DivisorSigma[0,#]==EulerPhi[#]&] (* _Harvey P. Dale_, Jun 28 2022 *)
%o A062516 (PARI) for(n=1,1000000, if(numdiv(n)*2==eulerphi(n),print(n),))
%Y A062516 Cf. A112954, A020488, A063469, A063470.
%K A062516 nonn,fini,full
%O A062516 1,1
%A A062516 _Jason Earls_, Jul 13 2001
%E A062516 "full" keyword from _Max Alekseyev_, Mar 01 2010