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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 (list; graph; refs; listen; history; text; internal format)
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

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

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

Cf. A089120, A014442, A078897.

Sequence in context: A133910 A066441 A300384 * A173398 A104404 A162512

Adjacent sequences:  A252887 A252888 A252889 * A252891 A252892 A252893

KEYWORD

nonn

AUTHOR

Michel Lagneau, Dec 24 2014

STATUS

approved

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Last modified May 19 06:41 EDT 2019. Contains 323386 sequences. (Running on oeis4.)