

A308664


Numbers k such that tau(k) and phi(k) are the legs of a Pythagorean triple.


0




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


LINKS

Table of n, a(n) for n=1..5.


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

Cf. A000005, A000010, A020488, A062516, A063469, A063470, A112954.
Sequence in context: A078210 A174628 A316098 * A184065 A259734 A294736
Adjacent sequences: A308661 A308662 A308663 * A308665 A308666 A308667


KEYWORD

nonn,fini,more


AUTHOR

Antonio Roldán, Jul 14 2019


STATUS

approved



