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

Author

Arkadiusz Wesolowski, Jul 25 2016

Keywords

• nonn
• hard
• more

Examples

			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
		

Crossrefs

Cf. A078303, A273947.

Programs

Mathematica

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

PARI

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

Formula

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

Extensions

a(8) was found in 2001 by Robert Silverman

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