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

0,1

Links

Table of n, a(n) for n=0..11.

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

Example

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

Mathematica

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

Prog

(PARI) a(n) = numdiv(2^2^n+1)
(Magma) [DivisorSigma(0, 2^2^n + 1): n in [1..100]]
(GAP) List(List([0..11], n->2^(2^n)+1), i->Number(DivisorsInt(i))); # Muniru A Asiru, Nov 03 2018

Crossrefs

Cf. A000005, A000215.

Sequence in context: A001306 A260984 A108105 * A063468 A010336 A054537

Adjacent sequences: A321210 A321211 A321212 * A321214 A321215 A321216

Keyword

nonn,more,hard

Author

Jinyuan Wang, Oct 31 2018

Extensions

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

Status

approved