

A193562


Number of divisors of n^4+1.


3



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
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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: A082508 A327730 A303809 * A249868 A255311 A075526
Adjacent sequences: A193559 A193560 A193561 * A193563 A193564 A193565


KEYWORD

nonn,easy


AUTHOR

Jonathan Vos Post, Aug 09 2011


STATUS

approved



