A342899 Smallest number that is the sum of five positive n-th powers in four ways.

53, 1252, 20995, 287618651, 351060139210

Offset

2,1

Links

Table of n, a(n) for n=2..6.

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.

Example

53 = 1^2 + 1^2 + 1^2 + 1^2 + 7^2
   = 1^2 + 1^2 + 1^2 + 5^2 + 5^2
   = 1^2 + 2^2 + 4^2 + 4^2 + 4^2
   = 1^2 + 3^2 + 3^2 + 3^2 + 5^2
   = 2^2 + 2^2 + 2^2 + 4^2 + 5^2.
1252 = 1^3 + 1^3 + 5^3 + 5^3 + 10^3
     = 1^3 + 2^3 + 3^3 + 6^3 + 10^3
     = 3^3 + 3^3 + 7^3 + 7^3 +  8^3
     = 3^3 + 4^3 + 6^3 + 6^3 +  9^3.
20995 = 1^4 + 1^4 + 1^4 + 4^4 + 12^4
      = 2^4 + 3^4 + 3^4 + 3^4 + 12^4
      = 2^4 + 6^4 + 9^4 + 9^4 +  9^4
      = 4^4 + 6^4 + 7^4 + 7^4 + 11^4.
287618651 =  8^5 + 21^5 + 27^5 + 27^5 + 48^5
          =  9^5 + 13^5 + 26^5 + 37^5 + 46^5
          = 11^5 + 12^5 + 23^5 + 41^5 + 44^5
          = 11^5 + 20^5 + 22^5 + 30^5 + 48^5.
351060139210 =  8^6 + 50^6 + 53^6 + 56^6 + 81^6
             = 18^6 + 43^6 + 49^6 + 64^6 + 80^6
             = 27^6 + 31^6 + 56^6 + 62^6 + 80^6
             = 35^6 + 36^6 + 38^6 + 73^6 + 76^6.

Crossrefs

Cf. A230563, A342893-A342903.

Sequence in context: A157618 A093982 A091548 * A017769 A017716 A180365

Adjacent sequences: A342896 A342897 A342898 * A342900 A342901 A342902

Keyword

nonn,hard,more

Author

N. J. A. Sloane, Apr 04 2021

Extensions

a(5) from Robert Israel, Apr 07 2021

a(6) from Michael S. Branicky, May 08 2021

Status

approved