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A248516 n^2+1 divided by its largest prime factor.

%I A248516 #32 Jun 22 2015 13:50:54
%S A248516 1,1,2,1,2,1,10,5,2,1,2,5,10,1,2,1,10,25,2,1,26,5,10,1,2,1,10,5,2,17,
%T A248516 26,25,10,13,2,1,10,85,2,1,58,5,50,13,2,29,130,5,2,41,2,5,10,1,34,1,
%U A248516 250,5,2,13,2,5,10,17,2,1,10,125,2,169,2,85,130,1,58
%N A248516 n^2+1 divided by its largest prime factor.
%C A248516 a(n)=1 iff n^2+1 is prime (see A002496).
%C A248516 Conjecture: The Fibonacci numbers in the sequence are 1, 2, 5, 13, 34, 89, 233, 377, 610, 1597, 4181, 10946, 28657, 75025, 121393, 196418, ... including all of A001519.
%H A248516 Michel Lagneau, <a href="/A248516/b248516.txt">Table of n, a(n) for n = 1..10000</a>
%F A248516 a(n) = A002522(n)/A014442(n).
%F A248516 a(n) = A052126(1+n^2). - _R. J. Mathar_, Jun 18 2015
%p A248516 A248516 := proc(n)
%p A248516     n^2+1 ;
%p A248516     %/A006530(%) ;
%p A248516 end proc:
%p A248516 seq(A248516(n),n=1..20) ; # _R. J. Mathar_, Jun 18 2015
%t A248516 Table[(n^2 + 1)/FactorInteger[n^2 + 1][[-1, 1]], {n, 75}] (* _Michael De Vlieger_, Jun 19 2015 *)
%o A248516 (PARI) a(n) = my(x=n^2+1); my(f=factor(x)); x/f[#f~,1]; \\ _Michel Marcus_, Jun 18 2015
%Y A248516 Cf. A001519, A002522, A014442, A245236.
%K A248516 nonn,easy
%O A248516 1,3
%A A248516 _Michel Lagneau_, Jun 18 2015