login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 3 17:49 EDT 2022. Contains 357237 sequences. (Running on oeis4.)