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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. 1

%I

%S 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 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 29,4,30,12,31,3,32,0,33,13,34,5,35,14,36,0,37,1

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

%C a(n) = floor(n / A089120(n)).

%C 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 Michel Lagneau, <a href="/A249122/b249122.txt">Table of n, a(n) for n = 1..20000</a>

%e a(8) = 1 because 30^2 + 1 = 17*53 and floor(30/17) = 1.

%e Or a(8) = a(A247340(2)) = 1.

%p with(numtheory):

%p for n from 1 to 200 do:

%p p:=n^2+1:x:=factorset(p):d:=floor(n/x[1]):

%p printf(`%d, `, d):

%p od:

%t Table[Floor[n/ FactorInteger[n^2+1][[ 1, 1]]], {n, 100}]

%o (PARI) a(n) = n\factor(n^2+1)[1, 1]; \\ _Michel Marcus_, Oct 25 2014

%Y Cf. A002496, A089120, A134406, A247340.

%K nonn

%O 1,5

%A _Michel Lagneau_, Oct 21 2014

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Last modified April 5 12:52 EDT 2020. Contains 333241 sequences. (Running on oeis4.)