A275377 Number of odd prime factors (with multiplicity) of generalized Fermat number 3^(2^n) + 1.

0, 1, 1, 2, 1, 1, 1, 5, 4, 6

Offset: 0

Author

Arkadiusz Wesolowski, Jul 25 2016

Keywords

• nonn
• hard
• more

Examples

			b(n) = (3^(2^n) + 1)/2.
Complete Factorizations
b(0) = 2
b(1) = 5
b(2) = 41
b(3) = 17*193
b(4) = 21523361
b(5) = 926510094425921
b(6) = 1716841910146256242328924544641
b(7) = 257*275201*138424618868737*3913786281514524929*P21
b(8) = 12289*8972801*891206124520373602817*P90
b(9) = 134382593*22320686081*12079910333441*100512627347897906177*P93*P101
		

Links

• Arkadiusz Wesolowski, A 93-digit prime factor of b(9)

Crossrefs

Cf. A059919, A273945.

Programs

PARI

a001222(n) = bigomega(n)
a059919(n) = 3^(2^n)+1
a(n) = if(n==0, 0, a001222(a059919(n))-1) \\ Felix Fröhlich, Jul 25 2016

Formula

a(n) = A001222(A059919(n)) - 1 for n > 0. - Felix Fröhlich, Jul 25 2016

Extensions

a(9) was found in 2008 by Tom Womack