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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

a(5) > 10^23. - Jon E. Schoenfield, Apr 19 2014

REFERENCES

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.

LINKS

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

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, etc.

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 * A231832 A193157 A235604

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 July 23 01:55 EDT 2014. Contains 244849 sequences.