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

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, 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, 1, 6, 1, 3, 4, 1, 2, 2, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1

Offset: 1

Author

Michel Lagneau, Dec 24 2014

Keywords

• nonn

Comments

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

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

Examples

			a(7)=4 because 7^2 + 1 = 50 and 5 is 4 times a factor:
2^2+1 = 5;
3^2+1 = 10 = 2*5;
7^2+1 = 50 = 2*5*5 (two times).
		

Links

• Michel Lagneau, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A089120, A014442, A078897.

Programs

Maple

with(numtheory): with(padic,ordp):
f:= proc(n) local p ,q, n0;
  q:=factorset(n^2+1);n0:=nops(q);p:= q[n0];
  add(ordp(k^2+1, p), k=1..n);
end proc:
seq(f(n), n=1.. 100);
# Using code from Robert Israel adapted for this sequence. See A078897.