A259036 - OEIS

%I #20 Sep 08 2022 08:46:13

%S 1,2,5,5,17,13,37,10,13,41,101,61,29,17,197,113,257,29,25,181,401,26,

%T 97,53,577,313,677,73,157,421,53,37,41,109,89,613,1297,137,85,761,

%U 1601,58,353,50,149,1013,73,65,461,1201,61,1301,541,281,2917,89,3137,65

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

%C Subsequence of A033677.

%C a(n) = n^2+1 if n^2+1 is prime (see A005574) or n=0. - _Michel Marcus_, Jul 01 2015

%C 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 Robert Israel, <a href="/A259036/b259036.txt">Table of n, a(n) for n = 0..10000</a>

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

%e 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 f:= proc(n) local m,k;

%p   m:= n^2+1;

%p   min(select(t -> t^2 >= m, numtheory:-divisors(m)))

%p end proc:

%p map(f, [$0..100]); # _Robert Israel_, Dec 03 2019

%t Table[Select[Divisors[n^2+1], # >= Sqrt[n^2+1] &, 1] // First, {n, 80}]

%o (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 (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 Cf. A002522, A005574, A033677, A085722.

%K nonn,easy,look

%O 0,2

%A _Michel Lagneau_, Jun 17 2015