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

%I A297305 #70 Jul 28 2025 08:59:06
%S A297305 5,10,15,20,25,30,31,35,40,45,50,55,60,62,65,70,75,80,85,89,90,93,95,
%T A297305 100,103,105,110,115,120,124,125,130,135,140,145,150,155,160,165,170,
%U A297305 175,178,180,185,186,190,195,200,205,206,210,215,217,220,225,230,233
%N A297305 Numbers k such that k^4 can be written as a sum of five positive 4th powers.
%C A297305 If k is in the sequence, then k*m is in the sequence for every positive integer m.
%H A297305 Jinyuan Wang, <a href="/A297305/b297305.txt">Table of n, a(n) for n = 1..500</a>
%H A297305 Titus Piezas III, <a href="https://web.archive.org/web/20091022203521/http://www.geocities.com/titus_piezas/ramanujan_page10.html">Ramanujan and the Quartic Equation 2^4+2^4+3^4+4^4+4^4 = 5^4</a>, 2005.
%H A297305 Jinyuan Wang, <a href="/A297305/a297305.txt">All solutions to k^4 = a^4 + b^4 + c^4 + d^4 + e^4 with k < 999</a>.
%H A297305 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DiophantineEquation4thPowers.html">Diophantine Equation 4th Powers</a>.
%H A297305 <a href="/index/Di#Diophantine">Index to sequences related to Diophantine equations</a> (4,1,5)
%e A297305     5^4 =  2^4 +  2^4 +  3^4 +  4^4 +   4^4 (=       625).
%e A297305    31^4 = 10^4 + 10^4 + 10^4 + 17^4 +  30^4 (=    923521).
%e A297305    89^4 = 10^4 + 35^4 + 52^4 + 60^4 +  80^4 (=  62742241).
%e A297305   103^4 =  4^4 + 15^4 + 50^4 + 50^4 + 100^4 (= 112550881).
%Y A297305 Cf. A000583, A003294, A023042, A301601, A386494.
%K A297305 nonn
%O A297305 1,1
%A A297305 _Seiichi Manyama_, Mar 16 2018
%E A297305 a(43)-a(57) from _Jon E. Schoenfield_, Mar 17 2018