A093507 -id:A093507 - cp's OEIS frontend

A057229 a(n) = ab = xy with (a-b) = (x+y) = A020882(n) (a>b, a>0, b>0, x>0, y>0), gcd(a, b) = gcd(x, y) = 1.

6, 30, 60, 84, 210, 210, 180, 630, 330, 504, 924, 1320, 546, 1386, 1560, 2340, 990, 2730, 840, 2574, 4620, 1224, 1716, 3570, 5610, 7140, 4290, 1710, 5016, 7956, 7980, 2730, 7854, 10374, 2310, 11970, 6630, 10920, 12540, 4080, 3036, 11856, 8970

Offset: 0

Naohiro Nomoto, Sep 19 2000

nonn

The quadratics in X, X^2 - S*X -+ P, where S=A020882(n), P=A057229(n) are each factorizable into two factors, all four being distinct: X^2 - S*X - P = (X - a)*(X + b). X^2 - S*X + P = (X - x)*(X - y). - Lekraj Beedassy, Apr 30 2004

Areas of primitive Pythagorean triangles sorted on hypotenuse A020882, then on perimeter A093507. - Lekraj Beedassy, Aug 18 2006

			E.g. a(1)=6=6*1=3*2, (6-1)=(3+2)=5=A020882(1), gcd(6,1)=gcd(3,2)=1

P. Yiu, Factorizable x^2 + px -+ q, Recreational Mathematics, pp. 58/360.

Cf. A020882, A008846, A024406, A024365.

A093508 Semiperimeter of primitive Pythagorean triangles sorted on hypotenuse A020882(n).

Original entry on oeis.org

6, 15, 20, 28, 35, 42, 45, 63, 66, 72, 77, 88, 99, 91, 104, 117, 110, 130, 120, 143, 165, 156, 153, 170, 187, 204, 195, 190, 221, 209, 228, 210, 238, 247, 266, 231, 255, 273, 285, 304, 276, 299, 322, 336, 345, 323, 357, 368, 325, 350, 342, 391, 400, 414, 425

Offset: 1

Lekraj Beedassy, May 14 2004

nonn

For ordered semiperimeter of primitive Pythagorean triangles see A020886.

a(n)=A093507/2.

cp's OEIS Frontend

A057229 a(n) = ab = xy with (a-b) = (x+y) = A020882(n) (a>b, a>0, b>0, x>0, y>0), gcd(a, b) = gcd(x, y) = 1.

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A093508 Semiperimeter of primitive Pythagorean triangles sorted on hypotenuse A020882(n).

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Author

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cp's OEIS Frontend

A057229 a(n) = a*b = x*y with (a-b) = (x+y) = A020882(n) (a>b, a>0, b>0, x>0, y>0), gcd(a, b) = gcd(x, y) = 1.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A093508 Semiperimeter of primitive Pythagorean triangles sorted on hypotenuse A020882(n).

Views

Author

Keywords

Comments

Formula

A057229 a(n) = ab = xy with (a-b) = (x+y) = A020882(n) (a>b, a>0, b>0, x>0, y>0), gcd(a, b) = gcd(x, y) = 1.