OFFSET
1,1
COMMENTS
FORMULA
1st family (A324746): The primitive terms are defined by p*q, p < q, with phi(p*q) = (p-1)*(q-1) = m^2. The general terms are defined by k = p^(2s+1) * q^(2t+1), s,t >= 0, with phi(k) = (p^s * q^t * m)^2.
2nd family (A324747): The primitive terms are defined by p^2 * q, p <> q, with phi(p^2 * q) = p*(p-1)*(q-1) = m^2. The general terms are defined by k = p^(2s ) * q^(2t+1), s >= 1, t >= 0, with phi(k) = (p^(s-1) * q^t * m)^2.
EXAMPLE
1st family: 136 = 2^3 * 37 and phi(136) = 8^2.
2nd family: 652 = 2^2 * 163 and phi(652) = 18^2.
MAPLE
filter:= n -> issqr(numtheory:-phi(n)) and nops(numtheory:-factorset(n))=2:
select(filter, [$1..2000]); # Robert Israel, Mar 18 2019
MATHEMATICA
Select[Range[1400], And[PrimeNu[#] == 2, IntegerQ@ Sqrt@ EulerPhi@ #] &] (* Michael De Vlieger, Mar 21 2019 *)
PROG
(PARI) isok(n) = (omega(n)==2) && issquare(eulerphi(n)); \\ Michel Marcus, Mar 17 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Bernard Schott, Mar 12 2019
STATUS
approved