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

Author

Seiichi Manyama, Mar 16 2018

Keywords

• nonn

Comments

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

Examples

			    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).
		

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)

Crossrefs

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

Extensions

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