A321213 a(n) is the number of divisors of n-th Fermat number (A000215).

2, 2, 2, 2, 2, 4, 4, 4, 4, 8, 16, 32

Offset: 0

Author

Jinyuan Wang, Oct 31 2018

Keywords

• nonn
• more
• hard

Examples

			A000215(n) is prime for n=0 to 4, so a(n)= 2 for n=0 to 4.
		

Crossrefs

Cf. A000005, A000215.

Programs

GAP

List(List([0..11],n->2^(2^n)+1),i->Number(DivisorsInt(i))); # Muniru A Asiru, Nov 03 2018

Magma

[DivisorSigma(0, 2^2^n + 1): n in [1..100]]

Mathematica

Table[DivisorSigma[0, 2^2^n + 1], {n, 120}]

PARI

a(n) = numdiv(2^2^n+1)

Formula

a(n) = A000005(A000215(n)). - Omar E. Pol, Oct 31 2018

a(n) = 2^A046052(n) for squarefree A000215(n). - Amiram Eldar, Oct 31 2018

Extensions

a(10)-a(11) from Amiram Eldar, Oct 31 2018