A185002 Numbers k such that P(k^2+1) > P((k+1)^2+1) where P(n) (A006530) is the largest prime factor of n.

4, 6, 10, 11, 12, 14, 16, 17, 20, 22, 24, 26, 29, 30, 33, 36, 37, 40, 42, 45, 46, 49, 51, 52, 54, 56, 59, 61, 62, 63, 66, 67, 69, 71, 72, 74, 79, 82, 84, 85, 88, 90, 92, 94, 95, 97, 98, 101, 102, 103, 104, 106, 108, 110, 113, 116, 118, 120, 121, 122, 124, 126

Offset: 1

Author

Michel Lagneau, Jan 23 2012

Keywords

• nonn

Examples

			11 is in the sequence because 11^2+1 = 2*61 and 12^2+1 = 5*29 => 61 > 29.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A014442, A002522, A006530, A070087, A185011.

Programs

Mathematica

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

PARI

r=2;for(k=1,1e3,t=factor((k+1)^2+1)[,1];t=t[#t];if(tCharles R Greathouse IV, Jan 23 2012