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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 (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 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, 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

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Last modified June 14 21:27 EDT 2021. Contains 345041 sequences. (Running on oeis4.)