OFFSET
1,4
COMMENTS
Length of row n of A001265.
LINKS
Sean A. Irvine, Table of n, a(n) for n = 1..1206 (terms 1..500 from T. D. Noe)
J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
Alex Kontorovich, Jeff Lagarias, On Toric Orbits in the Affine Sieve, arXiv:1808.03235 [math.NT], 2018.
R. Mestrovic, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof, arXiv preprint arXiv:1202.3670 [math.HO], 2012-2018.
S. S. Wagstaff, Jr., The Cunningham Project
Eric Weisstein's World of Mathematics, Mersenne Number
FORMULA
EXAMPLE
a(4) = 2 because 2^4 - 1 = 15 = 3*5.
From Gus Wiseman, Jul 04 2019: (Start)
The sequence of Mersenne numbers together with their prime indices begins:
1: {}
3: {2}
7: {4}
15: {2,3}
31: {11}
63: {2,2,4}
127: {31}
255: {2,3,7}
511: {4,21}
1023: {2,5,11}
2047: {9,24}
4095: {2,2,3,4,6}
8191: {1028}
16383: {2,14,31}
32767: {4,11,36}
65535: {2,3,7,55}
131071: {12251}
262143: {2,2,2,4,8,21}
524287: {43390}
1048575: {2,3,3,5,11,13}
(End)
MATHEMATICA
a[q_] := Module[{x, n}, x=FactorInteger[2^n-1]; n=Length[x]; Sum[Table[x[i][2], {i, n}][j], {j, n}]]
a[n_Integer] := PrimeOmega[2^n - 1]; Table[a[n], {n, 200}] (* Vladimir Joseph Stephan Orlovsky, Jul 22 2011 *)
PROG
(PARI) a(n)=bigomega(2^n-1) \\ Charles R Greathouse IV, Apr 01 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved