OFFSET
1,3
COMMENTS
Pollack and Pomerance proved that if phi(a) = b^m, then m = 2 occurs only on a set of density 0.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Paul Pollack and Carl Pomerance, Square values of Euler's function, Bulletin of the London Mathematical Society, Vol. 46, No. 2 (2014), pp. 403-414, alternative link.
EXAMPLE
a(11) = 41 because phi(k*11) is not a perfect square for 0 < k < 41 and phi(41*11) = 20^2.
MAPLE
f:= proc(n) local k;
for k from 1 do
if issqr(numtheory:-phi(k*n)) then return k fi
od
end proc:
map(f, [$1..100]); # Robert Israel, Jan 12 2017
MATHEMATICA
a[n_] := Module[{k = 1}, While[!IntegerQ[Sqrt[EulerPhi[k*n]]], k++]; k]; Array[a, 80] (* Amiram Eldar, Jul 13 2019 *)
PROG
(PARI) a(n) = {my(k = 1); while (!issquare(eulerphi(k*n)), k++); k; }
CROSSREFS
KEYWORD
nonn
AUTHOR
Altug Alkan, Jan 12 2017
STATUS
approved