This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A193432 #54 Apr 17 2025 23:18:38
%S A193432 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,
%T A193432 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,
%U A193432 8,8,4,6,4,8,16,2,8,4,8,4,4,4,8,6,16,2
%N A193432 Number of divisors of n^2 + 1.
%H A193432 Seiichi Manyama, <a href="/A193432/b193432.txt">Table of n, a(n) for n = 0..10000</a>
%H A193432 Anton Shakov, <a href="https://arxiv.org/abs/2405.03552">Polynomials in Z[x] whose divisors are enumerated by SL_2(N_0)</a>, arXiv:2405.03552 [math.NT], 2024.
%F A193432 a(n) = A000005(A002522(n)). - _Michel Marcus_, Mar 16 2018
%e A193432 a(7) = 6 because 7^2 + 1 = 50 and the 6 divisors are {1, 2, 5, 10, 25, 50}.
%p A193432 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:
%t A193432 Array[DivisorSigma[0, #^2 + 1] &, 85, 0] (* _Michael De Vlieger_, Mar 17 2018 *)
%o A193432 (PARI) a(n) = numdiv(n^2+1); \\ _Michel Marcus_, Mar 16 2018
%o A193432 (Python)
%o A193432 from sympy import divisor_count
%o A193432 def A193432(n): return divisor_count(n**2+1) # _Chai Wah Wu_, Apr 17 2025
%Y A193432 Cf. A000005, A002522, A128428, A193330, A193433.
%K A193432 nonn
%O A193432 0,2
%A A193432 _Michel Lagneau_, Jul 28 2011