The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A046051 Number of prime factors of Mersenne number M(n) = 2^n - 1 (counted with multiplicity). 43
 0, 1, 1, 2, 1, 3, 1, 3, 2, 3, 2, 5, 1, 3, 3, 4, 1, 6, 1, 6, 4, 4, 2, 7, 3, 3, 3, 6, 3, 7, 1, 5, 4, 3, 4, 10, 2, 3, 4, 8, 2, 8, 3, 7, 6, 4, 3, 10, 2, 7, 5, 7, 3, 9, 6, 8, 4, 6, 2, 13, 1, 3, 7, 7, 3, 9, 2, 7, 4, 9, 3, 14, 3, 5, 7, 7, 4, 8, 3, 10, 6, 5, 2, 14, 3, 5, 6, 10, 1, 13, 5, 9, 3, 6, 5, 13, 2, 5, 8 (list; graph; refs; listen; history; text; internal format)
 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 Mobius transform of A085021. - T. D. Noe, Jun 19 2003 a(n) = A001222(A000225(n)). - Michel Marcus, Jun 06 2019 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) MAPLE with(numtheory): P:=proc(n) local a, k; a:=ifactors(2^n-1)[2]; add(a[k][2], k=1..nops(a)); end: seq(P(i), i=1..99); # Paolo P. Lava, Jul 18 2018 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 bigomega(b^n-1): A057951 (b=10), A057952 (b=9), A057953 (b=8), A057954 (b=7), A057955 (b=6), A057956 (b=5), A057957 (b=4), A057958 (b=3), this sequence (b=2). Cf. A000043, A000668, A001348, A054988, A054989, A054990, A054991, A054992, A085021. Cf. A000225, A001221, A001222, A046800, A049093, A059305, A325610, A325611, A325612, A325625. Sequence in context: A319149 A344462 A321887 * A025812 A263001 A109698 Adjacent sequences:  A046048 A046049 A046050 * A046052 A046053 A046054 KEYWORD nonn AUTHOR STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 19 12:20 EDT 2022. Contains 353833 sequences. (Running on oeis4.)