|
|
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^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)
|
|
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
|
|
|
|