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A051584 Number of integer-sided triangles of area n. 5
0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,12

COMMENTS

If integer-sided triangle has integer area, area is divisible by 6.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10085

PROG

(PARI)

A051585(n) = sum(z=sqrtint(sqrtint(192*n^2)-1)+1, sqrtint(9*(64*n^2+5)\20), sum(y=z\2+1, z, my(t=(y*z)^2-(12*n)^2, x); if(issquare(t, &t), (issquare(y^2+z^2-2*t, &x) && x<=y) + (t && issquare(y^2+z^2+2*t, &x) && x<=y), 0))); \\ From A051585 by Charles R Greathouse IV

A051584(n) = if((n%6), 0, A051585(n/6)); \\ Antti Karttunen, Aug 23 2019

CROSSREFS

Cf. A051585, A051586.

Sequence in context: A028661 A028714 A028653 * A028645 A028710 A178926

Adjacent sequences:  A051581 A051582 A051583 * A051585 A051586 A051587

KEYWORD

nonn

AUTHOR

David W. Wilson

EXTENSIONS

Data section extended up to a(120) by Antti Karttunen, Aug 23 2019

STATUS

approved

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Last modified June 25 03:59 EDT 2022. Contains 354835 sequences. (Running on oeis4.)