

A063903


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


3



1, 3, 14, 42, 248, 594, 744, 4064, 7668, 12192, 16775168, 50325504, 4294934528, 12884803584, 68719345664, 206158036992
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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 n is in the sequence and 3 doesn't divide n then 3*n 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. 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, Mar 25 2007


LINKS

Table of n, a(n) for n=1..16.


PROG

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


CROSSREFS

Cf. A000043, A000668, A020492.
Sequence in context: A000550 A124650 A291138 * A305009 A115005 A058389
Adjacent sequences: A063900 A063901 A063902 * A063904 A063905 A063906


KEYWORD

more,nonn


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



