A006515 Mersenne numbers with at most 2 prime factors. (Formerly M2695)

3, 7, 31, 127, 2047, 8191, 131071, 524287, 8388607, 2147483647, 137438953471, 2199023255551, 576460752303423487, 2305843009213693951, 147573952589676412927, 9671406556917033397649407, 618970019642690137449562111, 158456325028528675187087900671

Offset

1,1

References

John Brillhart, D. H. Lehmer, J. L. Selfridge, Bryant Tuckerman and S. S. Wagstaff, Jr., Factorizations of b^n +- 1. Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 2nd edition, 1985; and later supplements.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Amiram Eldar, Table of n, a(n) for n = 1..53

John Brillhart, D. H. Lehmer, J. L. Selfridge, Bryant Tuckerman and S. S. Wagstaff, Jr., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.

C. K. Caldwell, Mersenne primes.

S. S. Wagstaff, Jr., The Cunningham Project.

Formula

a(n) = A000225(A006514(n)). - Amiram Eldar, Sep 19 2023

Maple

A006515 := proc(n) local i;
i := 2^(ithprime(n))-1:
if (nops(numtheory[factorset](i)) < 3) then
   return i
fi: end: seq(A006515(n), n=1..19);

Mathematica

Select[Array[2^Prime[#] - 1 &, 25], PrimeOmega@ # <= 2 &] (* Michael De Vlieger, May 04 2017 *)

Crossrefs

Cf. A000225, A001348, A006514.

Sequence in context: A105768 A084924 A001348 * A093535 A081093 A057612

Adjacent sequences: A006512 A006513 A006514 * A006516 A006517 A006518

Keyword

nonn

Author

N. J. A. Sloane.

Extensions

More terms from Sean A. Irvine, May 04 2017

Status

approved