A297305 Numbers k such that k^4 can be written as a sum of five positive 4th powers.

5, 10, 15, 20, 25, 30, 31, 35, 40, 45, 50, 55, 60, 62, 65, 70, 75, 80, 85, 89, 90, 93, 95, 100, 103, 105, 110, 115, 120, 124, 125, 130, 135, 140, 145, 150, 155, 160, 165, 170, 175, 178, 180, 185, 186, 190, 195, 200, 205, 206, 210, 215, 217, 220, 225, 230, 233

Offset

1,1

Comments

If k is in the sequence, then k*m is in the sequence for every positive integer m.

Links

Jinyuan Wang, Table of n, a(n) for n = 1..500

Titus Piezas III, Ramanujan and the Quartic Equation 2^4+2^4+3^4+4^4+4^4 = 5^4, 2005.

Jinyuan Wang, All solutions to k^4 = a^4 + b^4 + c^4 + d^4 + e^4 with k < 999.

Eric Weisstein's World of Mathematics, Diophantine Equation 4th Powers.

Index to sequences related to Diophantine equations (4,1,5)

Example

    5^4 =  2^4 +  2^4 +  3^4 +  4^4 +   4^4 (=       625).
   31^4 = 10^4 + 10^4 + 10^4 + 17^4 +  30^4 (=    923521).
   89^4 = 10^4 + 35^4 + 52^4 + 60^4 +  80^4 (=  62742241).
  103^4 =  4^4 + 15^4 + 50^4 + 50^4 + 100^4 (= 112550881).

Crossrefs

Cf. A000583, A003294, A023042, A301601, A386494.

Sequence in context: A313732 A381337 A306236 * A182340 A313733 A076311

Adjacent sequences: A297302 A297303 A297304 * A297306 A297307 A297308

Keyword

nonn

Author

Seiichi Manyama, Mar 16 2018

Extensions

a(43)-a(57) from Jon E. Schoenfield, Mar 17 2018

Status

approved