A374418
a(n) is the smallest number which can be represented as the sum of 2 distinct positive n-th powers in exactly 3 ways, or -1 if no such number exists.
Original entry on oeis.org
7, 325, 87539319
Offset: 1
a(2) = 325 = 1^2 + 18^2 = 6^2 + 17^2 = 10^2 + 15^2.
a(3) = 87539319 = 167^3 + 436^3 = 228^3 + 423^3 = 255^3 + 414^3.
A338800
Smallest number that is the sum of two distinct n-th powers of primes in two different ways.
Original entry on oeis.org
16, 410, 6058655748, 3262811042
Offset: 1
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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