A275379 Number of prime factors (with multiplicity) of generalized Fermat number 6^(2^n) + 1.

1, 1, 1, 2, 3, 3, 3, 7, 3, 5

Offset

0,4

Links

Table of n, a(n) for n=0..9.

Formula

a(n) = A001222(A078303(n)). - Felix Fröhlich, Jul 25 2016

Example

b(n) = 6^(2^n) + 1.
Complete Factorizations
b(0) = 7
b(1) = 37
b(2) = 1297
b(3) = 17*98801
b(4) = 353*1697*4709377
b(5) = 2753*145601*19854979505843329
b(6) = 4926056449*447183309836853377*28753787197056661026689
b(7) = 257*763649*50307329*3191106049*2339340566463317436161*
       2983028405608735541756929*18247770097021321924017185281
b(8) = 18433*
       69615986569139423375849495295909549956813828853888948633601*P137
b(9) = 80897*3360769*12581314681802812884728041373153281*
       3513902440204553274892072241244613302018049*P311

Mathematica

Table[PrimeOmega[6^(2^n) + 1], {n, 0, 6}] (* Michael De Vlieger, Jul 26 2016 *)

Prog

(PARI) a(n) = bigomega(factor(6^(2^n)+1))

Crossrefs

Cf. A078303, A273947.

Sequence in context: A170895 A141479 A055081 * A109833 A132005 A222292

Adjacent sequences: A275376 A275377 A275378 * A275380 A275381 A275382

Keyword

nonn,hard,more

Author

Arkadiusz Wesolowski, Jul 25 2016

Extensions

a(8) was found in 2001 by Robert Silverman

a(9) was found in 2007 by Nestor de Araújo Melo

Status

approved