A374256 a(n) is the smallest number which can be represented as the sum of n distinct positive n-th powers in exactly 2 ways, or -1 if no such number exists.

-1, 65, 1009, 6834, 1158224, 19198660, 1518471174, 301963223843, 14599274102522, 1601155487573222

Offset: 1

Author

Ilya Gutkovskiy, Jul 01 2024

Keywords

• sign
• more

Examples

			a(2) = 65 = 1^2 + 8^2 = 4^2 + 7^2.
a(3) = 1009 = 1^3 + 2^3 + 10^3 = 4^3 + 6^3 + 9^3.
		

Crossrefs

Cf. A025303, A025400, A091414, A146756, A374226, A374257.

Programs

Maple

f:= proc(n) uses priqueue;
  local pq,w,t,g,i,count,newt;
  g:= proc(t) local i; [-add((t[i]+i)^n,i=1..n),op(t)] end proc;
  w:= [0$(n+1)];
  initialize(pq);
  insert(g([0$n]),pq);
  do
    t:= extract(pq);
    if t[1] = w[1] then return -t[1] fi;
    w:= t;
    for i from 2 to n+1 do
        if t[i]=t[-1] then
          newt:= g(t[2..-1] + [0$(i-2),1$(n+2-i)]);
        insert(newt,pq);
  fi od od;
end proc:
-1, seq(f(n),n=2..10); # Robert Israel, Jul 01 2024

Extensions

a(9)-a(10) from Robert Israel, Jul 01 2024