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A024361 Number of primitive Pythagorean triangles with leg n. 8
0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 2, 1, 0, 2, 1, 1, 0, 1, 2, 2, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 1, 2, 0, 2, 2, 1, 0, 2, 2, 1, 0, 1, 2, 2, 0, 1, 2, 1, 0, 2, 2, 1, 0, 2, 2, 2, 0, 1, 4, 1, 0, 2, 1, 2, 0, 1, 2, 2, 0, 1, 2, 1, 0, 2, 2, 2, 0, 1, 2, 1, 0, 1, 4, 2, 0, 2, 2, 1, 0, 2, 2, 2, 0, 2, 2, 1, 0, 2, 2, 1, 0, 1, 2, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,12

COMMENTS

Consider primitive Pythagorean triangles (A^2 + B^2 = C^2, (A, B) = 1, A <= B); sequence gives number of times A or B takes value n.

For n>1, a(n)=0 for n=A016825=2(mod 4).

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..20000

Ron Knott, Pythagorean Triples and Online Calculators

Eric Weisstein's World of Mathematics, Pythagorean Triple

EXAMPLE

a(12)=2 because 12 appears twice, in (A,B,C) = (5,12,13) and (12,35,37).

MATHEMATICA

Table[If[n == 1 || Mod[n, 4] == 2, 0, 2^(Length[FactorInteger[n]] - 1)], {n, 100}]

PROG

(PARI) A024361(n) = if(1==n||(2==(n%4)), 0, 2^(omega(n)-1)); \\ (after the Mathematica program) - Antti Karttunen, Nov 10 2018

CROSSREFS

Cf. A024362, A046079, A020883, A020884.

Sequence in context: A096419 A283616 A130182 * A305614 A190676 A135486

Adjacent sequences:  A024358 A024359 A024360 * A024362 A024363 A024364

KEYWORD

nonn

AUTHOR

David W. Wilson

EXTENSIONS

Incorrect comment removed by Ant King, Jan 28 2011

More terms from Antti Karttunen, Nov 10 2018

STATUS

approved

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Last modified December 13 23:26 EST 2018. Contains 318087 sequences. (Running on oeis4.)