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A278761 a(n) is the number of parallelepipeds with vertices with integer coordinates between 0 and n and diagonals from one corner to the opposite corner with an integer length. 0
0, 0, 1, 1, 1, 1, 2, 4, 5, 6, 6, 7, 10, 10, 11, 12, 15, 16, 19, 20, 23, 25, 28, 30, 33, 35, 38, 40, 44, 47, 52, 54, 57, 59, 63, 65, 71, 73, 79, 81, 86, 89, 98, 101, 106, 108, 114, 117, 126, 130, 137, 142, 147, 150, 159, 162, 173, 178, 182 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

LINKS

Table of n, a(n) for n=0..58.

FORMULA

Sides a,b,c should fulfill the conditions that (1) a^2+b^2+c^2=d^2 and (2) a, b, and c are positive, coprime, and not > n

EXAMPLE

n=8 : [1,2,2],[1,4,8],[2,3,6],[4,4,7],[6,6,7]

PROG

(Python)

def coprime(k, m, n):

    while m:

        k, m=m, k%m

    if k==1:return 1

    while k:

        n, k=k, n%k

    return n

oeis=[0]

for n in range(n):

    kv=[i**2 for i in range(2*n)]

    pyt=[]

    for a in range(1, n):

        for b in range(a, n+1):

            for c in range(b, n+1):

                if a**2+b**2+c**2 in kv and coprime(a, b, c)==1:

                    pyt.append([a, b, c, int((a**2+b**2+c**2)**0.5+0.1)])

    oeis.append(len(pyt))

print(pyt)

CROSSREFS

Sequence in context: A086370 A083788 A058317 * A287076 A100006 A196262

Adjacent sequences:  A278758 A278759 A278760 * A278762 A278763 A278764

KEYWORD

nonn

AUTHOR

Knut Ångström, Nov 27 2016

EXTENSIONS

Formula clarified by Harvey P. Dale, Dec 08 2017

STATUS

approved

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Last modified October 21 10:33 EDT 2018. Contains 316414 sequences. (Running on oeis4.)