|
|
A216784
|
|
a(n) is the number of prime divisors of n^2 + 1 of the form a^2 + 1.
|
|
1
|
|
|
1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 0, 1, 1, 2, 2, 1, 1, 1, 1, 3, 0, 1, 0, 3, 1, 1, 0, 1, 1, 2, 1, 2, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 1, 2, 2, 1, 0, 1, 2, 2, 1, 1, 0, 2, 1, 1, 1, 2, 1, 2, 1, 1, 0, 2
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
|
|
LINKS
|
|
|
EXAMPLE
|
a(13) = 3 because 13^2+1 = 170 = 2*5*17 with 3 divisors of the form a^2+1 such that 2 = 1^2+1, 5=2^2+1 and 17 = 4^2+1.
a(34) = 0 because 34^2+1 = 1157 = 13*89 and the prime divisors 13, 89 are not of the form a^2+1.
|
|
MAPLE
|
with(numtheory):for n from 1 to 100 do:x:=n^2+1:y:=factorset(x):n1:=nops(y):i:=0:for k from 1 to n1 do:z:=sqrt(y[k]-1):if z=floor(z) then i:=i+1:else fi:od: printf(`%d, `, i):od:
|
|
MATHEMATICA
|
a[n_] := Length @ Select[FactorInteger[n^2 + 1][[;; , 1]], IntegerQ @ Sqrt[# - 1] &]; Array[a, 100] (* Amiram Eldar, Sep 11 2019 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|