OFFSET
1,1
COMMENTS
Includes all n == 182 or 443 (mod 625). In particular, the sequence has positive asymptotic density. # Robert Israel, Oct 06 2016
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
239 is in the sequence because 239^2+1 = 57122 = 2*13^4;
27493 is in the sequence because 27493^2+1 = 755865050 = 2*5^2*17^4*181.
MAPLE
N:= 100000: # to get all terms <= N
res:= {}:
p:= 2;
while p^4 <= N^2+1 do
for v in map(t -> subs(t, n), [msolve(n^2+1, p^4)]) do
res:= res union {seq(k*p^4+v, k = 0 .. (N-v)/p^4)}
od;
p:= nextprime(p);
od:
sort(convert(res, list)); # Robert Israel, Oct 06 2016
MATHEMATICA
Select[Range[2, 13000], Max[Transpose[FactorInteger[#^2+1]][[2]]]>3&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Nov 02 2012
STATUS
approved