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A281187 Totient numbers whose squares are not totient numbers.

%I A281187 #15 Mar 25 2017 17:15:21
%S A281187 22,46,58,78,82,92,102,106,138,164,166,172,178,190,212,226,238,262,
%T A281187 282,310,316,328,332,344,346,356,358,366,382,388,418,442,452,478,498,
%U A281187 502,506,508,562,586,598,606,618,620,632,656,658,676,692,712,718,742,796,808,822,838,856,862,884,886,970,976
%N A281187 Totient numbers whose squares are not totient numbers.
%C A281187 Members of A002202 whose squares are in A007617.
%C A281187 All terms are even.
%C A281187 Contains 2*p if p is a Sophie Germain prime (A005384) such that 4*p^2+1 is composite. In particular this is the case for Sophie Germain primes == 1 or 4 (mod 5).
%H A281187 Robert Israel, <a href="/A281187/b281187.txt">Table of n, a(n) for n = 1..4000</a>
%e A281187 22 is a term because 22 = phi(23) and 22^2 = 484 is not a totient.
%e A281187 83^2 * 2^k is a term for 5 < k < 34.
%p A281187 N:= 1000: # to get all terms <= N
%p A281187 M:= fsolve(n/(exp(gamma)*log(log(n))+3/log(log(n))) = N, n=4..N^2):
%p A281187 Totients:= select(`<=`,{seq(numtheory:-phi(n),n=1..M)},N):
%p A281187 R:= select(t -> numtheory:-invphi(t^2) = [], Totients):
%p A281187 sort(convert(R,list));
%o A281187 (PARI) lista(nn) = {for(n=1, nn,if(istotient(n) && !istotient(n^2), print1(n,", ")));}
%Y A281187 Cf. A000010, A002202, A005384, A007617.
%K A281187 nonn
%O A281187 1,1
%A A281187 _Robert Israel_ and _Altug Alkan_, Jan 16 2017