A193433 Sum of the divisors of n^2+1.

1, 3, 6, 18, 18, 42, 38, 93, 84, 126, 102, 186, 180, 324, 198, 342, 258, 540, 434, 546, 402, 756, 588, 972, 578, 942, 678, 1332, 948, 1266, 972, 1596, 1302, 1980, 1260, 1842, 1298, 2484, 1842, 2286, 1602, 2613, 2124, 3534, 2100, 3042, 2220, 4536, 2772, 3606

Offset: 0

Author

Michel Lagneau, Jul 28 2011

Keywords

• nonn

Examples

			a(7) = 93 because 7^2+1 = 50 and the sum of the 6 divisors { 1, 2, 5, 10, 25, 50} is 93.
		

Links

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

Crossrefs

Cf. A000203, A002522, A193432.

Programs

Maple

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

Mathematica

Table[Total[Divisors[n^2 + 1]], {n, 0, 100}] (* T. D. Noe, Jul 28 2011 *)
DivisorSigma[1,Range[0,50]^2+1] (* Harvey P. Dale, Aug 03 2020 *)

PARI

a(n) = sigma(n^2+1); \\ Michel Marcus, Mar 17 2018

Python

from sympy import divisor_sigma
def A193433(n): return divisor_sigma(n**2+1) # Chai Wah Wu, Apr 17 2025

Formula

a(n) = A000203(A002522(n)). - Michel Marcus, Mar 16 2018