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 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. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified July 27 11:45 EDT 2021. Contains 346304 sequences. (Running on oeis4.)