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

0,2

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.

Links

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

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.

Example

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

Mathematica

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

Prog

(PARI) a(n) = numdiv(n^4+1); \\ Michel Marcus, Feb 09 2020
(Magma) [NumberOfDivisors(n^4+1):n in [0..90]]; // Marius A. Burtea, Feb 09 2020

Crossrefs

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

Sequence in context: A327730 A365348 A303809 * A249868 A255311 A075526

Adjacent sequences: A193559 A193560 A193561 * A193563 A193564 A193565

Keyword

nonn,easy

Author

Jonathan Vos Post, Aug 09 2011

Status

approved