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A016078 Smallest number that is sum of 2 positive n-th powers in 2 different ways. 3
4, 50, 1729, 635318657 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

If it exists, a(5) > 1.02*10^26 (see eqn. (27) at the Mathworld link). - Jon E. Schoenfield, Jan 05 2019

LINKS

Table of n, a(n) for n=1..4.

R. Alter, Computations and generalizations on a remark of Ramanujan, pp. 182-196 of "Analytic Number Theory (Philadelphia, 1980)", ed. M. I. Knopp, Lect. Notes Math., Vol. 899, 1981.

Eric Weisstein's World of Mathematics, Diophantine Equation--5th Powers

FORMULA

a(n) <= A230561(n) for n > 1, with equality at least for n = 2, and inequality at least for n = 3. - Jonathan Sondow, Oct 24 2013

EXAMPLE

4 = 1^1 + 3^1 = 2^1 + 2^1;

50 = 1^2 + 7^2 = 5^2 + 5^2,

1729 = 1^3 + 12^3 = 9^3 + 10^3;

635318657 = 59^4 + 158^4 = 133^4 + 134^4.

MATHEMATICA

(* This is just an empirical verification *) Do[max = 4 + n^4; Clear[cnt]; cnt[_] = 0; smallest = Infinity;  Do[ cnt[an = x^n + y^n] += 1; If[cnt[an] == 2 && an < smallest, smallest = an], {x, 1, max}, {y, x, max}]; Print["a(", n, ") = ", smallest], {n, 1, 4}] (* Jean-Fran├žois Alcover, Aug 13 2013 *)

CROSSREFS

Cf. A046881, A230561.

Sequence in context: A201829 A201209 A026865 * A327229 A231832 A193157

Adjacent sequences:  A016075 A016076 A016077 * A016079 A016080 A016081

KEYWORD

nonn,nice,hard,more

AUTHOR

Robert G. Wilson v, Dec 11 1999

STATUS

approved

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Last modified April 3 19:43 EDT 2020. Contains 333198 sequences. (Running on oeis4.)