

A016078


Smallest number that is sum of 2 positive nth powers in 2 different ways.


3




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. 182196 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}] (* JeanFrançois 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



