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A252890 Number of times the greatest prime factor of n^2 + 1 is a factor in all numbers <= n.

%I A252890 #10 Dec 25 2014 03:58:28
%S A252890 1,1,2,1,1,1,4,2,1,1,1,1,2,1,1,1,2,3,1,1,3,1,1,1,1,1,1,1,1,2,2,2,1,1,
%T A252890 1,1,1,6,1,1,4,1,3,1,1,2,7,1,1,2,1,1,1,1,2,1,9,1,1,1,1,1,1,1,1,1,1,4,
%U A252890 1,6,1,3,4,1,2,2,1,1,1,1,1,1,4,1,1,1,1
%N A252890 Number of times the greatest prime factor of n^2 + 1 is a factor in all numbers <= n.
%C A252890 The greatest prime factor is counted with multiplicity (see the example).
%C A252890 a(n)=1 iff n^2 + 1 is prime.
%H A252890 Michel Lagneau, <a href="/A252890/b252890.txt">Table of n, a(n) for n = 1..10000</a>
%e A252890 a(7)=4 because 7^2 + 1 = 50 and 5 is 4 times a factor:
%e A252890 2^2+1 = 5;
%e A252890 3^2+1 = 10 = 2*5;
%e A252890 7^2+1 = 50 = 2*5*5 (two times).
%p A252890 with(numtheory): with(padic,ordp):
%p A252890 f:= proc(n) local p ,q, n0;
%p A252890   q:=factorset(n^2+1);n0:=nops(q);p:= q[n0];
%p A252890   add(ordp(k^2+1, p), k=1..n);
%p A252890 end proc:
%p A252890 seq(f(n), n=1.. 100);
%p A252890 # Using code from Robert Israel adapted for this sequence. See A078897.
%Y A252890 Cf. A089120, A014442, A078897.
%K A252890 nonn
%O A252890 1,3
%A A252890 _Michel Lagneau_, Dec 24 2014