A275378 Number of odd prime factors (with multiplicity) of generalized Fermat number 5^(2^n) + 1.

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

Offset: 0

Author

Arkadiusz Wesolowski, Jul 25 2016

Keywords

• nonn
• hard
• more

Examples

			b(n) = (5^(2^n) + 1)/2.
Complete Factorizations
b(0) = 3
b(1) = 13
b(2) = 313
b(3) = 17*11489
b(4) = 2593*29423041
b(5) = 641*75068993*241931001601
b(6) = 769*3666499598977*96132956782643741951225664001
b(7) = 257*23653200983830003298459393*P62
b(8) = 1655809*101199664791578113*4563566430220614493697*
       12025702000065183805751513732616276516181800961*P88
		

Links

• factordb.com, Status of 5^(2^n)+1.

Crossrefs

Cf. A199591, A273946.

Programs

Mathematica

Table[PrimeOmega[(5^(2^n) + 1)/2], {n, 0, 6}] (* Michael De Vlieger, Jul 26 2016 *)

PARI

a(n) = bigomega(factor((5^(2^n)+1)/2))

Formula

a(n) = A001222(A199591(n)) - 1. - Felix Fröhlich, Jul 25 2016