cp's OEIS Frontend

A239247 Numbers n such that n^4 can be written as a sum of five distinct positive 4th powers.

%I A239247 #32 Feb 16 2025 08:33:21
%S A239247 15,30,35,45,55,60,65,70,75,85,89,90,95,105,110,115,120,125,130,135,
%T A239247 140,145,150,155,165,170,175,178,180,185,190,195,205,210,215,220,225,
%U A239247 230,233,235,240,245,250,255,260,265,267,270,275,280,285,290,295,300
%N A239247 Numbers n such that n^4 can be written as a sum of five distinct positive 4th powers.
%C A239247 Every multiple of a term is a term.
%H A239247 Lars Blomberg, <a href="/A239247/b239247.txt">Table of n, a(n) for n = 1..7560 (terms < 10000)</a>
%H A239247 Lars Blomberg, <a href="/A239247/a239247.txt">Primitive solutions for terms < 10000</a>. Only the first solution found for each term is included.
%H A239247 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DiophantineEquation4thPowers.html">Diophantine Equation 4th Powers.</a>
%F A239247 a(1) = A130022(4).
%e A239247 15^4 = 4^4 + 6^4 + 8^4 + 9^4 + 14^4.
%e A239247 35^4 = 4^4 + 21^4 + 22^4 + 26^4 + 28^4.
%e A239247 55^4 = 2^4 + 13^4 + 16^4 + 44^4 + 48^4.
%e A239247 65^4 = 1^4 + 8^4 + 12^4 + 32^4 + 64^4.
%e A239247 85^4 = 2^4 + 13^4 + 32^4 + 34^4 + 84^4.
%e A239247 89^4 = 10^4 + 35^4 + 52^4 + 60^4 + 80^4.
%e A239247 95^4 = 6^4 + 48^4 + 66^4 + 67^4 + 78^4.
%e A239247 115^4 = 4^4 + 31^4 + 48^4 + 58^4 + 112^4.
%e A239247 125^4 = 8^4 + 11^4 + 26^4 + 84^4 + 118^4.
%e A239247 145^4 = 2^4 + 23^4 + 46^4 + 52^4 + 144^4.
%e A239247 155^4 = 6^4 + 39^4 + 88^4 + 96^4 + 144^4.
%e A239247 185^4 = 2^4 + 38^4 + 62^4 + 87^4 + 182^4.
%e A239247 205^4 = 4^4 + 133^4 + 142^4 + 146^4 + 156^4.
%e A239247 215^4 = 4^4 + 26^4 + 127^4 + 174^4 + 176^4.
%e A239247 233^4 = 40^4 + 65^4 + 94^4 + 150^4 + 220^4.
%e A239247 235^4 = 9^4 + 52^4 + 148^4 + 184^4 + 194^4.
%o A239247 (PARI) isok(n) = {ret = 0; for (x=1, sqrtnint(n^4\5, 4), for (y=x+1, sqrtnint((n^4 - x^4)\4, 4), for (z=y+1, sqrtnint((n^4 - x^4 - y^4)\3, 4), for (t=z+1, sqrtnint((n^4 - x^4 - y^4 - z^4)\2, 4), for (u=t+1, sqrtnint((n^4 - x^4 - y^4 - z^4 - t^4), 4), if (x^4+y^4+z^4+t^4+u^4 == n^4, print(n, ": ", x, ", ", y, ", ",z ,", ",t, ", ",u); ret = 1;);););););); return (ret);}
%Y A239247 Cf. A130022, A003828 (three 4th powers), A096739 (four 4th powers).
%K A239247 nonn
%O A239247 1,1
%A A239247 _Michel Marcus_, Mar 13 2014
%E A239247 Missing terms 15 and its multiples found by _Alois P. Heinz_, Mar 14 2014
%E A239247 More examples from _Michel Marcus_, Mar 18 2014
%E A239247 More terms from _Lars Blomberg_, Apr 05 2014