1,2

(1) If 2^p-1 is prime (a Mersenne prime) then 2^(p-2)*(2^p-1) is in the sequence - the proof is easy. So 2^(A000043-2)* (2^A000043-1) is a subsequence of this sequence. (2) If n is in the sequence and 3 doesn't divide n then 3*n is in the sequence. Hence If 2^p-1 is a Mersenne prime greater than 3 then 3*2^(p-2)*(2^p-1) is in the sequence. The statement (2) is an special case of " If gcd(m,n)=1 and m & n are in the sequence then m*n is in the sequence (*) ". (*) is correct because the three functions ud, phi & sigma are multiplicative. There is no further term up to 5.6*10^8. - Farideh Firoozbakht (mymontain(AT)yahoo.com), Mar 25 2007

(PARI) ud(n) = 2^omega(n); for(n=1, 10^8, if(ud(n)*eulerphi(n)==sigma(n), print(n)))

Cf. A000043, A000668.

Sequence in context: A055650 A000550 A124650 this_sequence A115005 A058389 A059672

Adjacent sequences: A063900 A063901 A063902 this_sequence A063904 A063905 A063906

more,nonn

Jason Earls (zevi_35711(AT)yahoo.com), Aug 30 2001

a(11) from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 10 2006

a(12) from Farideh Firoozbakht (mymontain(AT)yahoo.com), Mar 25 2007