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A051302 Numbers whose square can be expressed as the sum of two positive cubes in more than one way. 5
77976, 223587, 623808, 894348, 1788696, 2105352, 2989441, 4298427, 4672423, 4990464, 5986575, 6036849, 7154784, 8437832, 9747000, 14309568, 16842816, 23915528, 24147396, 24770529, 26745768, 27948375, 34387416, 34634719, 36570744, 37379384, 39923712, 47892600 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Observations regarding terms through a(64)=306761364: All are multiples of 7^2, 13^2, and/or 19^2. Other than 2, 3, 5 and 11, their only prime factors are 7, 13, 19, 31, 43, 61, 67, 79, 127, 151, and 181 (each of which exceeds a multiple of 6 by 1). None is a cube or higher power; the ones that are squares are a(7), a(12), a(17), a(19), a(20), a(32), a(33), a(41), a(49), a(55), and a(58). - Jon E. Schoenfield, Oct 08 2006

Many of the terms beyond a(64) have prime factors other than those found in a(1) through a(64); however, each term through a(774) has at most one distinct prime factor p > 5 that does not exceed a multiple of 6 by 1, and p, if such a prime factor exists, has a multiplicity m=3, with only a few exceptions: n=651 and n=713 (where p^m is 11^2), n=346 and n=770 (where p^m is 17^2), n=699 and n=740 (where p^m is 23^2), and n=741 (where p^m is 11^6). - Jon E. Schoenfield, Oct 20 2013

First differs from A145553 at A051302(172)=3343221000 where 3343221000^2 = 279300^3 + 2234400^3 = 790020^3 + 2202480^3 = 1256850^3 + 2094750^3.

This sequence is the union of A145553 and A155961.

LINKS

Jon Schoenfield and Ray Chandler, Table of n, a(n) for n = 1..774

EXAMPLE

2989441^2 = 1729^3+20748^3 = 15561^3+17290^3, so 2989441 is in the sequence.

CROSSREFS

Cf. A050801, A001235, A011541, A145553, A155961.

Sequence in context: A061528 A210141 * A145553 A016819 A016855 A016975

Adjacent sequences:  A051299 A051300 A051301 * A051303 A051304 A051305

KEYWORD

nonn,nice

AUTHOR

Jud McCranie

EXTENSIONS

Definition corrected by Jon E. Schoenfield, Aug 27 2006

More terms from Jon E. Schoenfield, Oct 08 2006

Extended by Ray Chandler, Nov 22 2011

STATUS

approved

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Last modified November 28 04:34 EST 2014. Contains 250286 sequences.