A247129 Semiprimes n such that phi(n) is a square.

10, 34, 57, 74, 85, 185, 202, 219, 394, 451, 489, 505, 514, 629, 679, 802, 985, 1057, 1154, 1285, 1354, 1387, 1417, 1717, 2005, 2047, 2509, 2594, 2649, 2761, 2885, 3097, 3202, 3277, 3349, 3385, 3409, 3459, 3737, 4207, 4369, 4377, 4577

Offset: 1

Author

Charles R Greathouse IV, Nov 19 2014

Keywords

• nonn

Comments

Freiberg & Pomerance show that this sequence is infinite and a(n) << n^2 log^2 n.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Tristan Freiberg, Carl Pomerance, A note on square totients, arXiv:1410.8109 [math.NT], 2014.

Crossrefs

Cf. A039770, A221285, A002496.

Programs

PARI

is(n)=issquare(eulerphi(n))&&bigomega(n)==2

PARI

list(lim)=my(v=List()); forprime(p=2,sqrtint(lim\1), forprime(q=p+1, lim\p, if(issquare((p-1)*(q-1)), listput(v,p*q)))); Set(v)