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A259036
Smallest divisor of n^2+1 >= sqrt(n^2+1).
1
1, 2, 5, 5, 17, 13, 37, 10, 13, 41, 101, 61, 29, 17, 197, 113, 257, 29, 25, 181, 401, 26, 97, 53, 577, 313, 677, 73, 157, 421, 53, 37, 41, 109, 89, 613, 1297, 137, 85, 761, 1601, 58, 353, 50, 149, 1013, 73, 65, 461, 1201, 61, 1301, 541, 281, 2917, 89, 3137, 65
OFFSET
0,2
COMMENTS
Subsequence of A033677.
a(n) = n^2+1 if n^2+1 is prime (see A005574) or n=0. - Michel Marcus, Jul 01 2015
If n^2+1=p*q for primes p,q with p<q (see A085722), then a(n)=q. - Robert Israel, Dec 03 2019
LINKS
FORMULA
a(n) = A033677(A002522(n)).
EXAMPLE
a(7) = 10 because 7^2+1 = 2*5*5 and 2*5 = 10 is the smallest divisor >=sqrt(7^2+1) = 7.0710678118...
MAPLE
f:= proc(n) local m, k;
m:= n^2+1;
min(select(t -> t^2 >= m, numtheory:-divisors(m)))
end proc:
map(f, [$0..100]); # Robert Israel, Dec 03 2019
MATHEMATICA
Table[Select[Divisors[n^2+1], # >= Sqrt[n^2+1] &, 1] // First, {n, 80}]
PROG
(PARI) concat(1, vector(100, n, d=divisors(n^2+1); k=1; while(d[k]<sqrt(n^2+1), k++); d[k])) \\ Derek Orr, Jun 27 2015
(Magma) [Min([d:d in Divisors(k^2+1)|d ge Sqrt(k^2+1) ]):k in [0..60]]; // Marius A. Burtea, Dec 03 2019
CROSSREFS
KEYWORD
nonn,easy,look
AUTHOR
Michel Lagneau, Jun 17 2015
STATUS
approved