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A308664
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Numbers k such that tau(k) and phi(k) are the legs of a Pythagorean triple.
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0
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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EXAMPLE
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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).
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MATHEMATICA
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Select[Range[300], IntegerQ@Sqrt[DivisorSigma[0, #]^2 + EulerPhi[#]^2] &] (* Amiram Eldar, Jul 26 2019 *)
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PROG
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(PARI) for(i = 1, 2000, a = eulerphi(i); b = numdiv(i); if(issquare(a^2 + b^2), print1(i, ", ")))
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CROSSREFS
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KEYWORD
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nonn,fini,full
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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