A248746 a(n) is the index k of the greatest prime divisor A002313(k) of n^2 + 1.

1, 2, 2, 4, 3, 6, 2, 3, 7, 13, 9, 5, 4, 22, 15, 26, 5, 3, 20, 39, 4, 12, 8, 51, 31, 60, 10, 18, 41, 8, 6, 7, 14, 11, 54, 105, 16, 4, 65, 121, 5, 35, 6, 17, 83, 10, 4, 45, 97, 9, 106, 48, 29, 209, 11, 221, 3, 59, 133, 28, 138, 66, 38, 25, 155, 294, 43, 6, 174, 5

Offset: 1

Author

Michel Lagneau, Oct 13 2014

Keywords

• nonn

Comments

a(n) is the number k such that A002313(k) = A014442(n).

Examples

			a(5)=3 because A002313(3)=13 and 5^2+1 = 2*13 with A002313(3)= A014442(5).
		

Links

• Michel Lagneau, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A014442 (greatest prime divisor of n^2+1), A002313 (primes congruent to 1 or 2 modulo 4).

Cf. also A002522.

Programs

Maple

with(numtheory):T:=array(1..50000):T[1]:=2:kk:=1:nn:=10^5:
for i from 1 to nn do:
  p:=4*i+1:
  if type(p,prime)=true
  then
    kk:=kk+1:T[kk]:=p:
    else
    fi:
   od:
     for k from 1 to 5000 do:ii:=0:
      y:=factorset(k^2+1):n2:=nops(y):t:=y[n2]:
        for l from 1 to kk while(ii=0)do :
        if t=T[l]
         then
         printf(`%d, `,l):
         else
        fi:
     od:
    od: