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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.

%I A360306 #16 Feb 16 2025 08:34:04
%S A360306 1,635318657,811538,300834,185299,138595,143651,154292,197748,225733,
%T A360306 291269,374790,474071,586056,715192,857513,1057689,1330554,1602250,
%U A360306 1919146,2329547,2786843,3246204,3899260,4642700,5378141,6377822,7342638,8527103,9787839,11241455,12978656
%N 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.
%H A360306 Bert Dobbelaere, <a href="/A360306/b360306.txt">Table of n, a(n) for n = 1..79</a>
%H A360306 Bert Dobbelaere, <a href="/A360306/a360306.cpp.txt">C++ program</a>
%H A360306 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BiquadraticNumber.html">Biquadratic Number</a>
%e A360306 For n = 2: 635318657 = 59^4 + 158^4 = 133^4 + 134^4.
%e A360306 For n = 3: 811538 = 4^4 + 23^4 + 27^4 = 7^4 + 21^4 + 28^4 = 12^4 + 17^4 + 29^4.
%e A360306 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.
%Y A360306 Cf. A000583, A146756, A350241, A350270.
%K A360306 nonn
%O A360306 1,2
%A A360306 _Ilya Gutkovskiy_, Feb 02 2023
%E A360306 a(18)-a(19) from _Michael S. Branicky_, Feb 04 2023
%E A360306 More terms from _Bert Dobbelaere_, Feb 11 2023