A193432 Number of divisors of n^2 + 1.

1, 2, 2, 4, 2, 4, 2, 6, 4, 4, 2, 4, 4, 8, 2, 4, 2, 8, 6, 4, 2, 8, 4, 8, 2, 4, 2, 8, 4, 4, 4, 8, 6, 8, 4, 4, 2, 8, 6, 4, 2, 6, 4, 12, 4, 4, 4, 16, 4, 4, 4, 4, 4, 8, 2, 8, 2, 16, 4, 4, 4, 4, 4, 8, 4, 4, 2, 8, 8, 4, 6, 4, 8, 16, 2, 8, 4, 8, 4, 4, 4, 8, 6, 16, 2

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Formula

a(n) = A000005(A002522(n)). - Michel Marcus, Mar 16 2018

Example

a(7) = 6 because 7^2 + 1 = 50 and the 6 divisors are {1, 2, 5, 10, 25, 50}.

Maple

with(numtheory):for n from 0 to 110 do:n1:=nops(divisors(n^2+1)):s:=0:for m from 1 to n1 do: s:=s+1:od: printf(`%d, `, s):od:

Mathematica

Array[DivisorSigma[0, #^2 + 1] &, 85, 0] (* Michael De Vlieger, Mar 17 2018 *)

Prog

(PARI) a(n) = numdiv(n^2+1); \\ Michel Marcus, Mar 16 2018

Crossrefs

Cf. A000005, A002522, A128428, A193330, A193433.

Sequence in context: A306652 A239614 A358216 * A129089 A255201 A169594

Adjacent sequences: A193429 A193430 A193431 * A193433 A193434 A193435

Keyword

nonn

Author

Michel Lagneau, Jul 28 2011

Status

approved