This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
0 = (empty sum). 2 = 1^4 + 1^4. 635318657 = 59^4 + 158^4 = 133^4 + 134^4.
a(6) = 342172570 = 4^6 + 5^6 + 18^6 + 20^6 + 25^6
= 8^6 + 10^6 + 11^6 + 23^6 + 24^6
= 8^6 + 13^6 + 15^6 + 16^6 + 26^6.
a(6) = 201968338 = 2^6 + 3^6 + 14^6 + 18^6 + 19^6 + 22^6
= 2^6 + 10^6 + 14^6 + 15^6 + 18^6 + 23^6
= 4^6 + 6^6 + 10^6 + 11^6 + 21^6 + 22^6.
a(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.
a(4) = 54994 = 1^4 + 2^4 + 4^4 + 8^4 + 15^4
= 1^4 + 2^4 + 9^4 + 10^4 + 14^4
= 2^4 + 5^4 + 6^4 + 11^4 + 14^4
= 3^4 + 7^4 + 8^4 + 10^4 + 14^4.
a(6) = 2063792939 = 1^6 + 4^6 + 16^6 + 21^6 + 31^6 + 32^6
= 4^6 + 7^6 + 20^6 + 22^6 + 29^6 + 33^6
= 5^6 + 7^6 + 16^6 + 25^6 + 30^6 + 32^6
= 5^6 + 8^6 + 14^6 + 27^6 + 29^6 + 32^6.
a(6) = 349717731 = 2^6 + 6^6 + 7^6 + 17^6 + 20^6 + 22^6 + 23^6
= 2^6 + 8^6 + 10^6 + 11^6 + 16^6 + 21^6 + 25^6
= 5^6 + 8^6 + 10^6 + 11^6 + 14^6 + 23^6 + 24^6
= 5^6 + 8^6 + 13^6 + 14^6 + 15^6 + 16^6 + 26^6.
10 = 3 + 7 = 5 + 5. 338 = 7^2 + 17^2 = 13^2 + 13^2. 6058655748 = 61^3 + 1823^3 = 1049^3 + 1699^3. 3262811042 = 7^4 + 239^4 = 157^4 + 227^4.
16 = 3 + 13 = 5 + 11. 410 = 7^2 + 19^2 = 11^2 + 17^2. 6058655748 = 61^3 + 1823^3 = 1049^3 + 1699^3. 3262811042 = 7^4 + 239^4 = 157^4 + 227^4.
f:= proc(n) local S,P,p,pn,b;
S:= {}:
P:= {}:
p:= 1:
b:= infinity;
do
p:= nextprime(p);
pn:= p^n;
if pn > b then return b fi;
V:= select(`<`,map(`+`,P,pn),b);
newv:= V intersect S;
S:= S union V;
P:= P union {p^n};
if newv <> {} then
b:= min(newv);
S:= select(`<`,S,b);
P:= select(`<`,P, b);
fi;
od:
end proc:
map(f, [$1..4]); # Robert Israel, Nov 13 2020
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