A089122 Triangle read by rows in which row n gives prime factors of n^2 + 1.

2, 5, 2, 5, 17, 2, 13, 37, 2, 5, 5, 13, 2, 41, 101, 2, 61, 5, 29, 2, 5, 17, 197, 2, 113, 257, 2, 5, 29, 5, 13, 2, 181, 401, 2, 13, 17, 5, 97, 2, 5, 53, 577, 2, 313, 677, 2, 5, 73, 5, 157, 2, 421, 17, 53, 2, 13, 37, 5, 41, 2, 5, 109, 13, 89, 2, 613, 1297, 2, 5, 137, 5, 17, 2, 761

Offset: 1

Author

Cino Hilliard, Dec 05 2003

Keywords

• easy
• nonn
• tabf

Comments

Prime factors taken without multiplicity. - Harvey P. Dale, Dec 02 2014

Examples

			Triangle starts:
2;
5;
2, 5;
17;
2, 13;
37;
2, 5;
5, 13;
2, 41,;
101;
...
		

References

• H. Rademacher, Lectures on Elementary Number Theory, pp. 33-38.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A002496.

Programs

Mathematica

Flatten[Table[Transpose[FactorInteger[n^2+1]][[1]],{n,40}]] (* Harvey P. Dale, Dec 02 2014 *)

PARI

allasqp1(m) = { for(a=1,m, y=a^2 + 1; f = factor(y); v = component(f,1); ln = length(v); for(i=1,ln,print1(v[i]",")) ) }