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

1,1

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).

Links

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

Example

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.

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));

Prog

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

Crossrefs

Cf. A000010, A002202, A005384, A007617.

Sequence in context: A350321 A106838 A190614 * A335297 A158862 A161666

Adjacent sequences: A281184 A281185 A281186 * A281188 A281189 A281190

Keyword

nonn

Author

Robert Israel and Altug Alkan, Jan 16 2017

Status

approved