A217846 Numbers which are the sums of consecutive sixth powers.

0, 1, 64, 65, 729, 793, 794, 4096, 4825, 4889, 4890, 15625, 19721, 20450, 20514, 20515, 46656, 62281, 66377, 67106, 67170, 67171, 117649, 164305, 179930, 184026, 184755, 184819, 184820, 262144, 379793, 426449, 442074, 446170, 446899, 446963, 446964, 531441

Offset: 1

Author

T. D. Noe, Oct 23 2012

Keywords

• nonn
• easy

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Subsequences include A001014 and A008516.

Cf. A034705, A217843-A217850.

Programs

Mathematica

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]

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