A281187 Totient numbers whose squares are not totient numbers.

22, 46, 58, 78, 82, 92, 102, 106, 138, 164, 166, 172, 178, 190, 212, 226, 238, 262, 282, 310, 316, 328, 332, 344, 346, 356, 358, 366, 382, 388, 418, 442, 452, 478, 498, 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

Offset: 1

Author

Robert Israel and Altug Alkan, Jan 16 2017

Keywords

• nonn

Comments

Members of A002202 whose squares are in A007617.

All terms are even.

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).

Examples

			22 is a term because 22 = phi(23) and 22^2 = 484 is not a totient.
83^2 * 2^k is a term for 5 < k < 34.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..4000

Crossrefs

Cf. A000010, A002202, A005384, A007617.

Programs

Maple

N:= 1000: # to get all terms <= N
M:= fsolve(n/(exp(gamma)*log(log(n))+3/log(log(n))) = N, n=4..N^2):
Totients:= select(`<=`,{seq(numtheory:-phi(n),n=1..M)},N):
R:= select(t -> numtheory:-invphi(t^2) = [], Totients):
sort(convert(R,list));

PARI

lista(nn) = {for(n=1, nn,if(istotient(n) && !istotient(n^2), print1(n,", ")));}