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A275823 Least k such that n divides phi(k^2).

%I A275823 #18 Jul 17 2019 02:51:43
%S A275823 1,2,3,4,5,3,7,4,9,5,11,6,13,7,15,8,17,9,19,5,7,11,23,12,25,13,9,14,
%T A275823 29,15,31,8,33,17,35,18,37,19,13,10,41,7,43,22,45,23,47,12,49,25,51,
%U A275823 13,53,9,11,28,19,29,59,15,61,31,21,16,65,33,67,17,69,35,71,36,73,37,75,38,77,13,79,20
%N A275823 Least k such that n divides phi(k^2).
%H A275823 Robert Israel, <a href="/A275823/b275823.txt">Table of n, a(n) for n = 1..10000</a>
%F A275823 a(n) <= n.
%F A275823 From _Robert Israel_, Aug 10 2016: (Start)
%F A275823 a(n) >= sqrt(n).
%F A275823 If n is prime or the square of a prime, then a(n) = n.
%F A275823 If n = m^j, then a(n) <= m^ceiling((j+1)/2). (End)
%e A275823 a(54) = 9 because 54 divides phi(9^2) = 54.
%p A275823 N:= 100: # to get a(1)..a(N)
%p A275823 S:= {$1..N}: A:= 'A':
%p A275823 for k from 1 while S <> {} do
%p A275823    r:= numtheory:-phi(k^2);
%p A275823    E:= select(t -> r mod t = 0, S);
%p A275823    if E <> {} then
%p A275823      assign(seq(A[e],e=E) = seq(k ,e=E));
%p A275823      S:= S minus E;
%p A275823    fi
%p A275823 od:
%p A275823 seq(A[i],i=1..N); # _Robert Israel_, Aug 10 2016
%t A275823 Table[k = 1; While[! Divisible[EulerPhi[k^2], n], k++]; k, {n, 80}] (* _Michael De Vlieger_, Aug 10 2016 *)
%o A275823 (PARI) a(n) = {my(k=1); while(eulerphi(k^2) % n, k++); k; }
%Y A275823 Cf. A002618.
%K A275823 nonn,easy
%O A275823 1,2
%A A275823 _Altug Alkan_, Aug 10 2016