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

%I

%S 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 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 1,6,1,3,4,1,2,2,1,1,1,1,1,1,4,1,1,1,1

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

%C The greatest prime factor is counted with multiplicity (see the example).

%C a(n)=1 iff n^2 + 1 is prime.

%H Michel Lagneau, <a href="/A252890/b252890.txt">Table of n, a(n) for n = 1..10000</a>

%e a(7)=4 because 7^2 + 1 = 50 and 5 is 4 times a factor:

%e 2^2+1 = 5;

%e 3^2+1 = 10 = 2*5;

%e 7^2+1 = 50 = 2*5*5 (two times).

%p with(numtheory): with(padic,ordp):

%p f:= proc(n) local p ,q, n0;

%p q:=factorset(n^2+1);n0:=nops(q);p:= q[n0];

%p add(ordp(k^2+1, p), k=1..n);

%p end proc:

%p seq(f(n), n=1.. 100);

%p # Using code from Robert Israel adapted for this sequence. See A078897.

%Y Cf. A089120, A014442, A078897.

%K nonn

%O 1,3

%A _Michel Lagneau_, Dec 24 2014

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Last modified June 17 06:06 EDT 2019. Contains 324183 sequences. (Running on oeis4.)