|
|
A285283
|
|
Number of integers x such that the greatest prime factor of x^2 + 1 is at most A002313(n), the n-th prime not congruent to 3 mod 4.
|
|
3
|
|
|
1, 4, 9, 15, 22, 32, 41, 57, 74, 94, 120, 156
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
In other words, x^2 + 1 is A002313(n)-smooth.
Størmer shows that the number of such integers is finite for any n.
a(n) <= 3^n - 2^n follows from Størmer's argument.
a(n) <= (2^n-1)*(A002313(n)+1)/2 is implicit in Lehmer 1964.
Luca 2004 determines all integers x such that x^2 + 1 is 100-smooth, which is pushed to 200 by Najman 2010.
|
|
LINKS
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,hard,more
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|