A193562 Number of divisors of n^4+1.

1, 2, 2, 4, 2, 4, 2, 4, 4, 8, 4, 4, 4, 4, 4, 8, 2, 4, 4, 8, 2, 4, 4, 4, 2, 8, 4, 8, 2, 4, 4, 8, 4, 8, 2, 4, 4, 8, 4, 4, 4, 8, 4, 16, 8, 8, 2, 8, 2, 8, 4, 8, 4, 8, 2, 8, 2, 4, 4, 16, 8, 4, 4, 8, 8, 4, 8, 8, 4, 8, 8, 4, 4, 4, 2, 8, 8, 16, 4, 16, 2, 4, 2, 16, 4

Offset: 0

Author

Jonathan Vos Post, Aug 09 2011

Keywords

• nonn
• easy

Comments

This is to n^4+1 as A193432 is to n^2+1.

a(n) = 2 when n^4+1 is prime, iff n is in A037896.

Examples

			a(3) = 4 because 3^4+1 = 82, whose 4 factors are {1, 2, 41, 82}.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000005, A002523, A037896, A193432 (number of divisors of n^2+1).

Programs

Magma

[NumberOfDivisors(n^4+1):n in [0..90]]; // Marius A. Burtea, Feb 09 2020

Mathematica

DivisorSigma[0,Range[0,90]^4+1] (* Harvey P. Dale, May 05 2013 *)

PARI

a(n) = numdiv(n^4+1); \\ Michel Marcus, Feb 09 2020

Formula

a(n) = A000005(A002523(n)) = d(n^4+1) (also called tau(n^4+1) or sigma_0(n^4+1)), the number of divisors of n^4+1.