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A252890
Number of times the greatest prime factor of n^2 + 1 is a factor in all numbers <= n.
1
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
1,3
COMMENTS
The greatest prime factor is counted with multiplicity (see the example).
a(n)=1 iff n^2 + 1 is prime.
LINKS
EXAMPLE
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).
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.
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Dec 24 2014
STATUS
approved