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

1,1

Links

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

Example

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

Mathematica

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

Prog

(PARI) r=2; for(k=1, 1e3, t=factor((k+1)^2+1)[, 1]; t=t[#t]; if(t<r, print1(k", ")); r=t) \\ Charles R Greathouse IV, Jan 23 2012

Crossrefs

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

Sequence in context: A057670 A171615 A141780 * A110604 A109270 A187331

Adjacent sequences: A184999 A185000 A185001 * A185003 A185004 A185005

Keyword

nonn

Author

Michel Lagneau, Jan 23 2012

Status

approved