A248516 n^2+1 divided by its largest prime factor.

1, 1, 2, 1, 2, 1, 10, 5, 2, 1, 2, 5, 10, 1, 2, 1, 10, 25, 2, 1, 26, 5, 10, 1, 2, 1, 10, 5, 2, 17, 26, 25, 10, 13, 2, 1, 10, 85, 2, 1, 58, 5, 50, 13, 2, 29, 130, 5, 2, 41, 2, 5, 10, 1, 34, 1, 250, 5, 2, 13, 2, 5, 10, 17, 2, 1, 10, 125, 2, 169, 2, 85, 130, 1, 58

Offset: 1

Author

Michel Lagneau, Jun 18 2015

Keywords

• nonn
• easy

Comments

a(n)=1 iff n^2+1 is prime (see A002496).

Conjecture: The Fibonacci numbers in the sequence are 1, 2, 5, 13, 34, 89, 233, 377, 610, 1597, 4181, 10946, 28657, 75025, 121393, 196418, ... including all of A001519.

Links

• Michel Lagneau, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001519, A002522, A014442, A245236.

Programs

Maple

A248516 := proc(n)
    n^2+1 ;
    %/A006530(%) ;
end proc:
seq(A248516(n),n=1..20) ; # R. J. Mathar, Jun 18 2015

Mathematica

Table[(n^2 + 1)/FactorInteger[n^2 + 1][[-1, 1]], {n, 75}] (* Michael De Vlieger, Jun 19 2015 *)

PARI

a(n) = my(x=n^2+1); my(f=factor(x)); x/f[#f~,1]; \\ Michel Marcus, Jun 18 2015

Formula

a(n) = A002522(n)/A014442(n).

a(n) = A052126(1+n^2). - R. J. Mathar, Jun 18 2015