login
A193432
Number of divisors of n^2 + 1.
26
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
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
KEYWORD
nonn
AUTHOR
Michel Lagneau, Jul 28 2011
STATUS
approved