

A085705


Integers expressible as (x^3 + y^3 + z^3)/(x*y*z) with nonzero integers x, y and z. Alternatively, integers expressible as a/b + b/c + c/a with nonzero integers a, b and c.


1



3, 5, 6, 9, 10, 13, 14, 15, 16, 17, 18, 19, 20, 21, 26, 29, 30, 31, 35, 36, 38, 40, 41, 44, 47, 51, 53, 54, 57, 62, 63, 64, 66, 67, 69, 70, 71, 72, 73, 74, 76, 77, 83, 84, 86, 87, 92, 94, 96, 98, 99, 101, 102, 103, 105, 106, 107, 108, 109, 110, 112, 113, 116, 117, 119, 120, 122, 123, 124, 126, 127, 128, 129, 130, 132, 133, 136, 142, 143, 145, 147, 148, 149, 151, 154, 155, 156, 158, 159, 160, 161, 162, 164, 166, 167, 172, 174, 175, 177, 178, 181, 185, 186, 187, 189, 190, 191, 192, 195, 196, 197
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OFFSET

1,1


COMMENTS

A representation n=(x^3+y^3+z^3)/(x*y*z) is equivalent to 2 representations n=a/b+b/c+c/a, given by a=y^2*z,b=z^2*x,c=x^2*y and a=y*z^2,b=x*y^2,c=z*x^2. Dean Hickerson, Jul 14 2003. For each a(n)>5 there are infinitely many representations. David J. Rusin, Jul 15 2003.


LINKS

Table of n, a(n) for n=1..111.
Dave Rusin, For which values of n is a/b + b/c + c/a = n solvable? [Broken link]
Dave Rusin, For which values of n is a/b + b/c + c/a = n solvable? [Cached copy of html wrapper for paper but in pdf format (so none of the links work)]
Dave Rusin, For which values of n is a/b + b/c + c/a = n solvable? [Cached copy of .txt file]


EXAMPLE

15 is in the sequence because 15=(7^33^31^3)/(7*3*1)=(343271)/21=15. This is equivalent to 15=9/77/147+147/9 or 15=3/6363/49+49/3.
16=(70^331^39^3)/(70*31*9)=(34300029791729)/19530=16.


CROSSREFS

Cf. A072716 (representation by positive x, y, z).
Sequence in context: A018900 A126590 A140584 * A187417 A072716 A167384
Adjacent sequences: A085702 A085703 A085704 * A085706 A085707 A085708


KEYWORD

nonn


AUTHOR

Hugo Pfoertner, Jul 18 2003


EXTENSIONS

More terms from Dave Rusin, Jul 26, 2003


STATUS

approved



