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A063903
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ud(n)*phi(n)=sigma(n), ud(n) = A034444.
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3
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1, 3, 14, 42, 248, 594, 744, 4064, 7668, 12192, 16775168, 50325504
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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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 (mymontain(AT)yahoo.com), Mar 25 2007
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PROG
| (PARI) ud(n) = 2^omega(n); for(n=1, 10^8, if(ud(n)*eulerphi(n)==sigma(n), print(n)))
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CROSSREFS
| Cf. A000043, A000668.
Sequence in context: A055650 A000550 A124650 * A115005 A058389 A059672
Adjacent sequences: A063900 A063901 A063902 * A063904 A063905 A063906
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KEYWORD
| more,nonn
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AUTHOR
| Jason Earls (zevi_35711(AT)yahoo.com), Aug 30 2001
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EXTENSIONS
| a(11) from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 10 2006
a(12) from Farideh Firoozbakht (mymontain(AT)yahoo.com), Mar 25 2007
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