OFFSET
1,2
COMMENTS
k is always of the form 4*j + 1.
If k is in the sequence and m=2^(k+2)*3*(7*2^k-1) then phi(m)+sigma(m)=3m (m is in the sequence A011251). The proof is easy. - Farideh Firoozbakht, Mar 04 2005
REFERENCES
H. Riesel, "Prime numbers and computer methods for factorization", Progress in Mathematics, Vol. 57, Birkhäuser, Boston, 1985, Chap. 4, see pp. 381-384.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Wilfrid Keller, List of primes k.2^n - 1 for k < 300
H. C. Williams and C. R. Zarnke, A report on prime numbers of the forms M = (6a+1)*2^(2m-1)-1 and (6a-1)*2^(2m)-1, Math. Comp., 22 (1968), 420-422.
MATHEMATICA
Do[ If[ PrimeQ[7*2^n - 1], Print[n]], {n, 1, 2500}]
PROG
(PARI) v=[ ]; for(n=0, 2000, if(isprime(7*2^n-1), v=concat(v, n), )); v
CROSSREFS
KEYWORD
hard,nonn,more
AUTHOR
EXTENSIONS
More terms from Douglas Burke (dburke(AT)nevada.edu).
More terms from Hugo Pfoertner, Jun 23 2004
STATUS
approved