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

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

Offset

1,5

Comments

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

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.

Links

Michel Lagneau, Table of n, a(n) for n = 1..20000

Example

a(8) = 1 because 30^2 + 1 = 17*53 and floor(30/17) = 1.
Or a(8) = a(A247340(2)) = 1.

Maple

with(numtheory):
   for n from 1 to 200 do:
    p:=n^2+1:x:=factorset(p):d:=floor(n/x[1]):
    printf(`%d, `, d):
   od:

Mathematica

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

Prog

(PARI) a(n) = n\factor(n^2+1)[1, 1]; \\ Michel Marcus, Oct 25 2014

Crossrefs

Cf. A002496, A089120, A134406, A247340.

Sequence in context: A363898 A110514 A338503 * A135157 A360692 A135156

Adjacent sequences: A249119 A249120 A249121 * A249123 A249124 A249125

Keyword

nonn

Author

Michel Lagneau, Oct 21 2014

Status

approved