The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A072716 Integers expressible as (x^3 + y^3 + z^3)/xyz with positive integers x, y and z. (Alternatively, the integers expressible as x/y + y/z + z/x with positive integers x, y and z.) 2
 3, 5, 6, 9, 10, 13, 14, 17, 18, 19, 21, 26, 29, 30, 38, 41, 51, 53, 54, 57, 66, 67, 69, 73, 74, 77, 83, 86, 94, 101, 102, 105, 106, 110, 113, 117, 122, 126, 129, 130, 133, 142, 145, 147, 149, 154, 158, 161, 162, 166, 174 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS It is easy to see that the numbers of the form n^2 + 5 are included in this sequence for n = 0, 1, 2,.... It is known that any of the numbers below does not appear in the sequence: (a) multiples of 4, (b) numbers congruent to 7 mod 8, (c) numbers of the form 2^m*k + 3 with odd numbers m >= 3 and k >= 1. It is also known, on the other hand, that there are infinitely many numbers congruent to 1, 2, 3, 5, or 6 mod 8 included in the sequence. There are other parametric representations (like m^2+5) with positive a,b and c: (see 'Mma lines' for generating expressions): n=(m^2+33)/2: 17,21,29,41,57,77,101,129,161,197,237,281,329,381,437,497,..., n=m^4+8m^2+4m+13: ...,818,381,154,53,18,13,26,69,178,413,858,..., n=m^4-2m^3+4m^2+3: ...,978,451,174,51,10,3,6,19,66,195,478,... - Erik Dofs (erik.dofs(AT)swipnet.se), Mar 06 2004 REFERENCES Andrew Bremner and R. K. Guy, Two more representation problems, Proc. Edinburgh Math. Soc. vol. 40 1997 pp. 1-17. Erik Dofs, Solutions of x^3+y^3+z^3=nxyz, Acta Arith. LXXIII.3 (1995) LINKS 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 41 appears in the sequence because we can write 41 = (1^3 + 2^3 + 9^3)/(1*2*9). For n = 142, {x,y,z} = {6587432496387235561093636933115859813174, 53881756527432415186060525094013536917351, 222932371699623861287567763383948430761525} MATHEMATICA {n, x, y, z} = {(k^2 + 33)/2, {(k^4 + 6k^3 + 36k^2 + 98k + 147)/16, (k^4 - 6k^3 + 36k^2 - 98k + 147)/16, (k^2 + 147)/4}/GCD[(k^4 + 6k^3 + 36k^2 + 98k + 147)/16, (k^4 - 6k^3 + 36k^2 - 98k + 147)/16]} {n, x, y, z} = {k^4 + 8k^2 + 4k + 13, {k^6 + k^5 + 10k^4 + 11k^3 + 28k^2 + 27k + 13, k^6 - 3k^5 + 12k^4 - 19k^3 + 30k^2 - 21k + 9, 2k^2 - 2k + 38}/ GCD[k^6 + k^5 + 10k^4 + 11k^3 + 28k^2 + 27k + 13, k^6 - 3k^5 + 12k^4 - 19k^3 + 30k^2 - 21k + 9]} {n, x, y, z} = {k^4 - 2k^3 + 4k^2 + 3, {k^4 - 3k^3 + 6k^2 - 5k + 3, k^2 - k + 3, k^2 - 3k + 3}/GCD[k^2 - k + 3, k^2 - 3k + 3]} CROSSREFS Cf. A085705. Sequence in context: A140584 A085705 A187417 * A167384 A112649 A050083 Adjacent sequences:  A072713 A072714 A072715 * A072717 A072718 A072719 KEYWORD nonn,nice AUTHOR Tadaaki Ohno (t-ohno(AT)hyper.ocn.ne.jp), Aug 07 2002 EXTENSIONS More terms from Dave Rusin, Jul 26, 2003 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 1 20:48 EST 2020. Contains 338858 sequences. (Running on oeis4.)