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A057229
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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.
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2
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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
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OFFSET
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0,1
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COMMENTS
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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
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LINKS
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Table of n, a(n) for n=0..42.
P. Yiu, Factorizable x^2 + px -+ q, Recreational Mathematics, pp. 58/360.
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EXAMPLE
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E.g. a(1)=6=6*1=3*2, (6-1)=(3+2)=5=A020882(1), gcd(6,1)=gcd(3,2)=1
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CROSSREFS
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Cf. A020882, A008846, A024406, A024365.
Sequence in context: A239978 A024406 A024365 * A120734 A116360 A336219
Adjacent sequences: A057226 A057227 A057228 * A057230 A057231 A057232
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KEYWORD
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nonn
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AUTHOR
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Naohiro Nomoto, Sep 19 2000
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STATUS
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approved
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