A252476 Least index k such that n = A252486(k), minimal number of 6th powers that sum to k^6; or a(n)=0 if no such k exists.
1141, 251, 54, 39, 18, 17, 16, 14, 4, 13, 11
Offset: 7
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.
M:= 10^8:
R:= Vector(M,144, datatype=integer[4]):
for p from 1 to floor(M^(1/7)) do
p7:= p^7;
if p > 1 then A[p]:= R[p7] fi;
R[p7]:= 1;
for j from p7+1 to M do
R[j]:= min(R[j],1+R[j - p7]);
od
od:
F:= proc(n,k,ub)
local lb, m, bestyet, res;
if ub <= 0 then return -1 fi;
if n <= M then
if n = 0 then return 0
elif R[n] > ub then return -1
else return R[n]
fi
fi;
lb:= floor(n/k^7);
if lb > ub then return -1 fi;
bestyet:= ub;
for m from lb to 0 by -1 do
res:= procname(n-m*k^7, k-1, bestyet-m);
if res >= 0 then
bestyet:= res+m;
fi
od:
return bestyet
end proc:
for n from floor(M^(1/7))+1 to 50 do
A[n]:= F(n^7,n-1,144)
od:
seq(A[n],n=2..50); # Robert Israel, Aug 17 2015
a(n,verbose=0,m=7)={N=n^m;for(k=3,999,forvec(v=vector(k-1,i,[1,n\sqrtn(k+1-i,m)]),ispower(N-sum(i=1,k-1,v[i]^m),m,&K)&&K>0&&!(verbose&&print1("/*"n" "v"*/"))&&return(k),1))}
a(7) = 1141 because 1141^6 = 1077^6 + 894^6 + 702^6 + 474^6 + 402^6 + 234^6 + 74^6 and no integer smaller than 1141 can be expressed as the sum of 7 positive 6th powers.
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