OFFSET
1,2
COMMENTS
Conjecture: the sequence is infinite.
Let b(n) = Product_{k=1..n} A002496(k): 2, 10, 170, 6290, 635290, ...
b(1) divides k^2+1 for k = 1, 3, 5, ...
b(2) divides k^2+1 for k = 3, 7, 13, 17, 23, 27, 33, 37, 43, 47, 53, 57, 63, 67, 73, 77, 83, ...
b(3) divides k^2+1 for k = 13, 47, 123, 157, 183, 217, 293, 327, 353, 387, 463, 497, 523, ...
b(4) divides k^2+1 for k = 327, 1067, 2707, 2843, 3447, 3583, 5223, 5963, 6617, 7357, 8997, 9133, 9737, 9873, ...
b(5) divides k^2+1 for k = 36673, 38067, 66347, 141087, 217443, 240087, 292183, 314827, 320463, ...
MAPLE
with(numtheory):lst:={2}:nn:=100:
for i from 1 to nn do:
p:=i^2+1:
if isprime(p)
then
lst:=lst union {p}:
else fi:
od:
pr:=1:
for n from 1 to 7 do:
pr:=pr*lst[n]:ii:=0:
for j from 1 to 10^9 while(ii=0) do:
if irem(j^2+1, pr)=0
then
ii:=1:
printf("%d %d \n", n, j):
fi:
od:
od:
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Jul 29 2015
EXTENSIONS
a(8)-a(17) from Hiroaki Yamanouchi, Aug 15 2015
STATUS
approved