A259036 Smallest divisor of n^2+1 >= sqrt(n^2+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

Author

Michel Lagneau, Jun 17 2015

Keywords

• nonn
• easy
• look

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 pA085722), then a(n)=q. - Robert Israel, Dec 03 2019

Examples

			a(7) = 10 because 7^2+1 = 2*5*5 and 2*5 = 10 is the smallest divisor >=sqrt(7^2+1) = 7.0710678118...
		

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A002522, A005574, A033677, A085722.

Programs

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

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}]

PARI

concat(1,vector(100,n,d=divisors(n^2+1);k=1;while(d[k]Derek Orr, Jun 27 2015

Formula

a(n) = A033677(A002522(n)).