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A125734
Primes of the form 4*3^k + 1.
3
5, 13, 37, 109, 2917, 19131877, 57395629, 16210220612075905069, 3187367866510497232065375864429355521950801431840733951694899540869109890815626195932616388528013, 254244997489062154119688681828370010268347235132197783249391539881181660045297550875174703528321187968562717038040968333
OFFSET
1,1
COMMENTS
Venkataraman showed that, for every p of this form, 3p is a perfect totient number (cf. A082897).
REFERENCES
T. Venkataraman, Perfect totient number, The Mathematics Student, Vol. 43 (1975), p. 178. MR0447089.
LINKS
Paul Loomis, Michael Plytage and John Polhill, Summing up the Euler phi function, The College Mathematics Journal, Vol. 39, No. 1 (Jan. 2008), pp. 34-42 (see Corollary 3).
FORMULA
4*3^k + 1 where k belongs to A005537.
EXAMPLE
37 = 4*3^2 + 1 is a prime of this form. 973 = 4*3^5 + 1 = 7*139 is not a prime, so is not included in this sequence.
MATHEMATICA
Do[p = 4*3^i + 1; If[PrimeQ@p, Print@p], {i, 0, 300}] (* Robert G. Wilson v, Feb 20 2007 *)
CROSSREFS
Sequence in context: A182312 A071100 A199108 * A146925 A146452 A146062
KEYWORD
nonn
AUTHOR
David Eppstein, Feb 06 2007, Feb 07 2007
EXTENSIONS
2 more terms from Robert G. Wilson v, Feb 20 2007
STATUS
approved