A275383 Number of prime factors (with multiplicity) of generalized Fermat number 12^(2^n) + 1.

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

Offset: 0

Author

Arkadiusz Wesolowski, Jul 25 2016

Keywords

• nonn
• hard
• more

Examples

			b(n) = 12^(2^n) + 1.
Complete Factorizations
b(0) = 13
b(1) = 5*29
b(2) = 89*233
b(3) = 17*97*260753
b(4) = 153953*1200913648289
b(5) = 769*44450180997616192602560262634753
b(6) = 36097*81281*69619841*73389730593973249*P35
b(7) = 257*P136
b(8) = 8253953*295278642689*5763919006323142831065059613697*P96*P132
		

Links

• Arkadiusz Wesolowski, A 96-digit prime factor of b(8)

Crossrefs

Cf. A152585, A273950.

Programs

Mathematica

Table[PrimeOmega[12^(2^n) + 1], {n, 0, 7}] (* Michael De Vlieger, Jul 26 2016 *)

PARI

a(n) = bigomega(factor(12^(2^n)+1))

Formula

a(n) = A001222(A152585(n)). - Felix Fröhlich, Jul 25 2016

Extensions

a(8) was found in 2009 by Tom Womack