A185011 Numbers k such that P(k^2+1) < P((k+1)^2+1) where P(n) (A006530) is the largest prime factor of n.

1, 3, 5, 7, 8, 9, 13, 15, 18, 19, 21, 23, 25, 27, 28, 31, 32, 34, 35, 38, 39, 41, 43, 44, 47, 48, 50, 53, 55, 57, 58, 60, 64, 65, 68, 70, 73, 75, 76, 77, 78, 80, 81, 83, 86, 87, 89, 91, 93, 96, 99, 100, 105, 107, 109, 111, 112, 114, 115, 117, 119, 123, 125

Offset: 1

Author

Michel Lagneau, Jan 23 2012

Keywords

• nonn

Examples

			8 is in the sequence because 8^2+1 = 5*13 and 9^2+1 = 2*41 => 13 < 41.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A002522, A070089, A006530, A070087, A185002.

Programs

Mathematica

f[n_]:=FactorInteger[n^2+1][[-1,1]];Select[Range[125],f[#]