OFFSET
1,1
COMMENTS
The sequence is finite since for all large enough n, we have tau(n) < n^(1/4) and phi(n) > n^(3/4) while, if x < y are the legs of a Pythagorean triangle, we always have y < x^2/2. - Giovanni Resta, Jul 27 2019
From Resta's inequality it can be deduced that phi(n) <= 2304. Then it's easy to see that the sequence is full. - Max Alekseyev, May 30 2024
EXAMPLE
60 is in this sequence because tau(60) = 12 and phi(60) = 16, legs of the Pythagorean triple {12, 16, 20} (12^2 + 16^2 = 20^2).
MATHEMATICA
Select[Range[300], IntegerQ@Sqrt[DivisorSigma[0, #]^2 + EulerPhi[#]^2] &] (* Amiram Eldar, Jul 26 2019 *)
PROG
(PARI) for(i = 1, 2000, a = eulerphi(i); b = numdiv(i); if(issquare(a^2 + b^2), print1(i, ", ")))
CROSSREFS
KEYWORD
nonn,fini,full
AUTHOR
Antonio Roldán, Jul 14 2019
EXTENSIONS
"full" keyword added by Max Alekseyev, May 30 2024
STATUS
approved