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A094572 Number of pairs of integers x, y (of either sign) with x^2 - y^2 = n. 5
2, 0, 4, 2, 4, 0, 4, 4, 6, 0, 4, 4, 4, 0, 8, 6, 4, 0, 4, 4, 8, 0, 4, 8, 6, 0, 8, 4, 4, 0, 4, 8, 8, 0, 8, 6, 4, 0, 8, 8, 4, 0, 4, 4, 12, 0, 4, 12, 6, 0, 8, 4, 4, 0, 8, 8, 8, 0, 4, 8, 4, 0, 12, 10, 8, 0, 4, 4, 8, 0, 4, 12, 4, 0, 12, 4, 8, 0, 4, 12, 10, 0, 4, 8, 8, 0, 8, 8, 4, 0, 8, 4, 8, 0, 8, 16, 4, 0, 12, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The old entry with this sequence number was a duplicate of A058071.

REFERENCES

M. N. Huxley, Area, Lattice Points and Exponential Sums, Oxford, 1996; p. 236.

LINKS

Ray Chandler, Table of n, a(n) for n = 1..10000

N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

FORMULA

a(n) = 2d(n) if n is odd, = 2d(n/4) if n == 0 mod 4, otherwise 0, where d() = A000005().

a(n) = 2 * A112329(n). - Ray Chandler, Aug 23 2014

MAPLE

with(numtheory); f:=proc(n) if n mod 2 = 1 then RETURN(2*tau(n)); fi; if n mod 4 = 0 then RETURN(2*tau(n/4)); fi; 0; end;

MATHEMATICA

Table[If[OddQ[n], 2DivisorSigma[0, n], If[OddQ[n/2], 0, 2DivisorSigma[0, n/4]]], {n, 100}] (* Ray Chandler, Aug 23 2014 *)

CROSSREFS

Cf. A000005, A093061, A112329.

Sequence in context: A155984 A028609 A107490 * A323905 A079534 A229910

Adjacent sequences:  A094569 A094570 A094571 * A094573 A094574 A094575

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 02 2008

STATUS

approved

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Last modified June 19 16:48 EDT 2019. Contains 324222 sequences. (Running on oeis4.)