

A281187


Totient numbers whose squares are not totient numbers.


1



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
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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: A041966 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



