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%I #9 Apr 22 2020 00:16:16
%S 0,1,64,65,729,793,794,4096,4825,4889,4890,15625,19721,20450,20514,
%T 20515,46656,62281,66377,67106,67170,67171,117649,164305,179930,
%U 184026,184755,184819,184820,262144,379793,426449,442074,446170,446899,446963,446964,531441
%N Numbers which are the sums of consecutive sixth powers.
%H T. D. Noe, <a href="/A217846/b217846.txt">Table of n, a(n) for n = 1..1000</a>
%t nMax = 10^6; t = {0}; Do[k = n; s = 0; While[s = s + k^6; s <= nMax, AppendTo[t, s]; k++], {n, nMax^(1/6)}]; t = Union[t]
%o (PARI) list(lim)=my(v=List(apply(n->n^6, [0..sqrtnint(lim\=1,6)])),s); for(n=2,lim, s=n*(n-1)*(2*n-1)*(3*n^4-6*n^3+3*n+1)/42; if(s>lim,break); for(k=n,lim, s+=k^6-(k-n)^6; if(s>lim,break); listput(v,s))); Set(v) \\ _Charles R Greathouse IV_, Apr 22 2020
%Y Subsequences include A001014 and A008516.
%Y Cf. A034705, A217843-A217850.
%K nonn,easy
%O 1,3
%A _T. D. Noe_, Oct 23 2012
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