A006515 Mersenne numbers with at most 2 prime factors.
3, 7, 31, 127, 2047, 8191, 131071, 524287, 8388607, 2147483647, 137438953471, 2199023255551, 576460752303423487, 2305843009213693951, 147573952589676412927, 9671406556917033397649407, 618970019642690137449562111, 158456325028528675187087900671
Offset: 1
Keywords
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.
Programs
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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);
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Mathematica
Select[Array[2^Prime[#] - 1 &, 25], PrimeOmega@ # <= 2 &] (* Michael De Vlieger, May 04 2017 *)
Formula
Extensions
More terms from Sean A. Irvine, May 04 2017