|
| |
|
|
A046080
|
|
a(n) = number of integer sided right triangles with hypotenuse n.
|
|
24
| |
|
|
0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 2, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 4, 0, 0, 1, 0, 1, 0, 0, 1, 1, 2, 0, 0, 1, 0, 1, 0, 1, 0, 0, 4, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,25
|
|
|
COMMENTS
| a(n)=0 for n in A004144. - Lekraj Beedassy (blekraj(AT)yahoo.com), May 14 2004
|
|
|
REFERENCES
| A. H. Beiler, Recreations in the Theory of Numbers, New York: Dover, pp. 116-117, 1966.
|
|
|
LINKS
| Ron Knott, Pythagorean Triples and Online Calculators
F. Richman, Pythagorean Triples
Eric Weisstein's World of Mathematics, Pythagorean Triple
|
|
|
FORMULA
| Let n = 2^e_2 * product_i p_i^f_i * product_j q_j^g_j where p_i == 1 mod 4, q_j == 3 mod 4; then a(n) = (1/2)*(product_i (2*f_i + 1) - 1). - Beiler, corrected
8*a(n) + 4 = A046109(n) for n > 0. - Ralf Stephan, Mar 14 2004
|
|
|
MATHEMATICA
| a[1] = 0; a[n_] := With[{fi = Select[ FactorInteger[n], Mod[#[[1]], 4] == 1 & ][[All, 2]]}, (Times @@ (2*fi+1)-1)/2]; Table[a[n], {n, 1, 99}] (* From Jean-François Alcover, Feb 06 2012, after first formula )
|
|
|
CROSSREFS
| First differs from A083025 at n=65.
Cf. A046079, A046081, A024362, A009000. A088111 gives records; A088959 gives where records occur.
Sequence in context: A015964 A088950 A083025 * A170967 A035227 A049340
Adjacent sequences: A046077 A046078 A046079 * A046081 A046082 A046083
|
|
|
KEYWORD
| nonn,changed
|
|
|
AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
|
| |
|
|
