OFFSET
1,2
COMMENTS
From Farideh Firoozbakht, Mar 25 2007: (Start)
(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 k is in the sequence and 3 doesn't divide k then 3*k 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.
Statement (2) is a special case of "If gcd(m,k)=1 and m & k are in the sequence then m*k 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. (End)
PROG
(PARI) ud(n) = 2^omega(n); for(n=1, 10^8, if(ud(n)*eulerphi(n)==sigma(n), print(n)))
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Jason Earls, Aug 30 2001
EXTENSIONS
a(11) from R. J. Mathar, Nov 10 2006
a(12) from Farideh Firoozbakht, Mar 25 2007
a(13)-a(16) from Donovan Johnson, Mar 06 2013
STATUS
approved