

A063903


Numbers k such that ud(k)*phi(k) = sigma(k), ud(k) = A034444.


3



1, 3, 14, 42, 248, 594, 744, 4064, 7668, 12192, 16775168, 50325504, 4294934528, 12884803584, 68719345664, 206158036992
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

(1) If 2^p1 is prime (a Mersenne prime) then 2^(p2)*(2^p1) is in the sequence  the proof is easy. So 2^(A0000432)*(2^A0000431) 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^p1 is a Mersenne prime greater than 3 then 3*2^(p2)*(2^p1) 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)


LINKS



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



EXTENSIONS



STATUS

approved



