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A156668 Positive integers k such that k^2 = (m^5+n^5)/(m+n) for some co-prime integers m,n. 3
1, 11, 101, 13361, 1169341, 1612186411, 1624763543401, 20188985439712961, 240020196429554642201, 29891946989942513908518251, 3506790234728288196345900732301, 5190947078637547438603476743093680561 (list; graph; refs; listen; history; internal format)
OFFSET

1,2

COMMENTS

This sequence probably contains no more than 5 primes.

LINKS

Kevin Acres and David Broadhurst, Rational points on y^2 = x^3 + 10*x^2 + 5*x

FORMULA

Numerators of rational numbers (81*x^4+540*x^3-8370*x^2+33900*x-47975)/(9*x^2 - 150*x + 445)^2, where x ranges over abscissas of rational points on the elliptic curve y^2 = x^3 - 85/3*x + 1550/27.

EXAMPLE

13361 belongs to this sequence since 13361^2 = (35^5 + 123^5) / (35 + 123) with gcd(35,123)=1.

CROSSREFS

Cf. A156669, A156670, A186082.

Sequence in context: A089971 A082620 A199304 * A103992 A185949 A201074

Adjacent sequences:  A156665 A156666 A156667 * A156669 A156670 A156671

KEYWORD

nonn

AUTHOR

Max Alekseyev (maxale(AT)gmail.com), Feb 13 2009

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Last modified February 16 07:39 EST 2012. Contains 205881 sequences.