A360306 a(n) is the smallest positive integer which can be represented as the sum of n distinct nonzero fourth powers in exactly n ways, or -1 if no such integer exists.

1, 635318657, 811538, 300834, 185299, 138595, 143651, 154292, 197748, 225733, 291269, 374790, 474071, 586056, 715192, 857513, 1057689, 1330554, 1602250, 1919146, 2329547, 2786843, 3246204, 3899260, 4642700, 5378141, 6377822, 7342638, 8527103, 9787839, 11241455, 12978656

Offset: 1

Author

Ilya Gutkovskiy, Feb 02 2023

Keywords

• nonn

Examples

			For n = 2: 635318657 = 59^4 + 158^4 = 133^4 + 134^4.
For n = 3: 811538 = 4^4 + 23^4 + 27^4 = 7^4 + 21^4 + 28^4 = 12^4 + 17^4 + 29^4.
For n = 4: 300834 = 1^4 + 4^4 + 12^4 + 23^4 = 1^4 + 16^4 + 18^4 + 19^4 = 3^4 + 6^4 + 18^4 + 21^4 = 7^4 + 14^4 + 16^4 + 21^4.
		

Links

• Bert Dobbelaere, Table of n, a(n) for n = 1..79
• Bert Dobbelaere, C++ program
• Eric Weisstein's World of Mathematics, Biquadratic Number

Crossrefs

Cf. A000583, A146756, A350241, A350270.

Extensions

a(18)-a(19) from Michael S. Branicky, Feb 04 2023

More terms from Bert Dobbelaere, Feb 11 2023