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

%I A259036 #20 Sep 08 2022 08:46:13
%S A259036 1,2,5,5,17,13,37,10,13,41,101,61,29,17,197,113,257,29,25,181,401,26,
%T A259036 97,53,577,313,677,73,157,421,53,37,41,109,89,613,1297,137,85,761,
%U A259036 1601,58,353,50,149,1013,73,65,461,1201,61,1301,541,281,2917,89,3137,65
%N A259036 Smallest divisor of n^2+1 >= sqrt(n^2+1).
%C A259036 Subsequence of A033677.
%C A259036 a(n) = n^2+1 if n^2+1 is prime (see A005574) or n=0. - _Michel Marcus_, Jul 01 2015
%C A259036 If n^2+1=p*q for primes p,q with p<q (see A085722), then a(n)=q. - _Robert Israel_, Dec 03 2019
%H A259036 Robert Israel, <a href="/A259036/b259036.txt">Table of n, a(n) for n = 0..10000</a>
%F A259036 a(n) = A033677(A002522(n)).
%e A259036 a(7) = 10 because 7^2+1 = 2*5*5 and 2*5 = 10 is the smallest divisor >=sqrt(7^2+1) = 7.0710678118...
%p A259036 f:= proc(n) local m,k;
%p A259036   m:= n^2+1;
%p A259036   min(select(t -> t^2 >= m, numtheory:-divisors(m)))
%p A259036 end proc:
%p A259036 map(f, [$0..100]); # _Robert Israel_, Dec 03 2019
%t A259036 Table[Select[Divisors[n^2+1], # >= Sqrt[n^2+1] &, 1] // First, {n, 80}]
%o A259036 (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
%o A259036 (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
%Y A259036 Cf. A002522, A005574, A033677, A085722.
%K A259036 nonn,easy,look
%O A259036 0,2
%A A259036 _Michel Lagneau_, Jun 17 2015