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 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 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) 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 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

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Last modified June 6 15:49 EDT 2023. Contains 363148 sequences. (Running on oeis4.)