A234002 4n/A234001(n).

1, 1, 4, 4, 1, 1, 2, 4, 3, 1, 4, 4, 1, 1, 2, 8, 1, 3, 4, 4, 1, 1, 2, 4, 5, 1, 36, 4, 1, 1, 2, 16, 1, 1, 4, 12, 1, 1, 2, 4, 1, 1, 4, 4, 3, 1, 2, 8, 7, 5, 4, 4, 1, 9, 2, 4, 1, 1, 4, 4, 1, 1, 6, 32, 1, 1, 4, 4, 1, 1, 2, 12, 1, 1, 20, 4, 1, 1, 2, 8, 27, 1, 4, 4, 1, 1, 2, 4, 1, 3, 4, 4, 1, 1, 2

Offset

1,3

Comments

Please look into A234001 for a more detailed description.

If n is squarefree and n == 1 (mod 4) or n == 2 (mod 4), then a(n) = 1.

If p^2 divides n for some prime p, a(n) is a multiple of p.

If n == 3 (mod 8), then a(n) is a multiple of 4 because numbers of the form x^2+n*y^2 cannot have any prime factors that are congruent to 2+n (mod 2n) raised to an odd power.

If n == 7 (mod 8), then a(n) is a multiple of 2 because numbers of the form x^2+n*y^2 can have prime factors that are congruent to 2+n (mod 2n) raised to an odd power, but they cannot be congruent to 2 (mod 4). So, we need to characterize the prime factor of 2 from the remaining prime factors that are congruent to 2+n (mod 2n) separately.

Links

Table of n, a(n) for n=1..95.

Crossrefs

Cf. A000926, A232550, A232551, A234001.

Sequence in context: A307886 A351122 A214499 * A016496 A143253 A060036

Adjacent sequences: A233999 A234000 A234001 * A234003 A234004 A234005

Keyword

nonn,uned

Author

V. Raman, Dec 18 2013

Status

approved