A275381 Number of prime factors (with multiplicity) of generalized Fermat number 10^(2^n) + 1.

1, 1, 2, 2, 5, 4, 3, 4, 5

Offset: 0

Author

Arkadiusz Wesolowski, Jul 25 2016

Keywords

• nonn
• hard
• more

Examples

			b(n) = 10^(2^n) + 1.
Complete Factorizations
b(0) = 11
b(1) = 101
b(2) = 73*137
b(3) = 17*5882353
b(4) = 353*449*641*1409*69857
b(5) = 19841*976193*6187457*834427406578561
b(6) = 1265011073*
       15343168188889137818369*515217525265213267447869906815873
b(7) = 257*15361*453377*P116
b(8) = 10753*8253953*9524994049*73171503617*P225
		

Crossrefs

Cf. A072982, A080176.

Programs

Mathematica

Table[PrimeOmega[10^(2^n) + 1], {n, 0, 6}] (* Michael De Vlieger, Jul 26 2016 *)

PARI

a(n) = bigomega(factor(10^(2^n)+1))

Formula

a(n) = A001222(A080176(n)). - Felix Fröhlich, Jul 25 2016