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A249122 a(n) = floor(n / lpf(n^2 + 1)) where lpf(n^2 + 1) is the smallest prime divisor of n^2 + 1.

%I A249122 #14 Sep 13 2017 02:18:10
%S A249122 0,0,1,0,2,0,3,1,4,0,5,2,6,0,7,0,8,3,9,0,10,4,11,0,12,0,13,5,14,1,15,
%T A249122 6,16,2,17,0,18,7,19,0,20,8,21,3,22,1,23,9,24,1,25,10,26,0,27,0,28,11,
%U A249122 29,4,30,12,31,3,32,0,33,13,34,5,35,14,36,0,37,1
%N A249122 a(n) = floor(n / lpf(n^2 + 1)) where lpf(n^2 + 1) is the smallest prime divisor of n^2 + 1.
%C A249122 a(n) = floor(n / A089120(n)).
%C A249122 a(A002496(n)) = 0 and a(A247340(n)) = 1  where A002496 are the primes of form m^2 + 1 and A247340(n) = {3, 8, 30, 46, 50, 76, ...} are the numbers m such that m^2 + 1 = p*q, p and q primes => p | a^2+1 and q | b^2+1 for some a,b < m.
%H A249122 Michel Lagneau, <a href="/A249122/b249122.txt">Table of n, a(n) for n = 1..20000</a>
%e A249122 a(8) = 1 because 30^2 + 1 = 17*53 and floor(30/17) = 1.
%e A249122 Or a(8) = a(A247340(2)) = 1.
%p A249122 with(numtheory):
%p A249122    for n from 1 to 200 do:
%p A249122     p:=n^2+1:x:=factorset(p):d:=floor(n/x[1]):
%p A249122     printf(`%d, `, d):
%p A249122    od:
%t A249122 Table[Floor[n/ FactorInteger[n^2+1][[ 1, 1]]], {n, 100}]
%o A249122 (PARI) a(n) = n\factor(n^2+1)[1, 1]; \\ _Michel Marcus_, Oct 25 2014
%Y A249122 Cf. A002496, A089120, A134406, A247340.
%K A249122 nonn
%O A249122 1,5
%A A249122 _Michel Lagneau_, Oct 21 2014