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%I #15 Jun 03 2017 02:55:00
%S 4,6,10,11,12,14,16,17,20,22,24,26,29,30,33,36,37,40,42,45,46,49,51,
%T 52,54,56,59,61,62,63,66,67,69,71,72,74,79,82,84,85,88,90,92,94,95,97,
%U 98,101,102,103,104,106,108,110,113,116,118,120,121,122,124,126
%N Numbers k such that P(k^2+1) > P((k+1)^2+1) where P(n) (A006530) is the largest prime factor of n.
%H G. C. Greubel, <a href="/A185002/b185002.txt">Table of n, a(n) for n = 1..5000</a>
%e 11 is in the sequence because 11^2+1 = 2*61 and 12^2+1 = 5*29 => 61 > 29.
%t f[n_]:=FactorInteger[n^2+1][[-1,1]];Select[Range[125],f[#]>f[#+1]&]
%o (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
%Y Cf. A014442, A002522, A006530, A070087, A185011.
%K nonn
%O 1,1
%A _Michel Lagneau_, Jan 23 2012
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