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.
%I A270103 #50 Aug 07 2020 19:32:27
%S A270103 1,3,1,6,2,1,10,3,2,1,15,5,3,2,1,21,7,4,3,2,1,28,9,5,4,3,2,1,36,11,6,
%T A270103 5,4,3,2,1,45,13,7,6,5,4,3,2,1,55,16,9,7,6,5,4,3,2,1,66,19,11,8,7,6,5,
%U A270103 4,3,2,1
%N A270103 Array read by antidiagonals: T(n, k) is the sum of the integer part of the n-th roots of natural numbers less than k.
%D A270103 R. L. Graham, D. E. Knuth, and O. Patashnik, Concrete Mathematics, 2nd Edition, Addison-Wesley, 1994, Eq. 3.27 on page 87.
%D A270103 D. E. Knuth, The Art of Computer Programming, Vol. 1, 3rd Edition, Addison-Wesley, 1997, Ex. 43 of section 1.2.4.
%H A270103 M. Griffiths, <a href="http://www.jstor.org/stable/3621862">More Sums Involving the Floor Function</a>, Math. Gaz., 86 (2002), 285-287.
%H A270103 Maths StackExchange, <a href="https://math.stackexchange.com/q/1274748">Find a formula for Sum_{k=1..n} floor(sqrt(k))</a>, see achille hui formula.
%H A270103 Wikipedia, <a href="https://en.wikipedia.org/wiki/Faulhaber%27s_formula">Faulhaber's formula</a>
%F A270103 T(n,k) = Sum_{j=0..k} floor(j^(1/n)).
%F A270103 T(n,k) = (1+k)*floor(k^(1/n)) - (1/(n+1))*Sum_{j=1..n+1} (1 + floor(k^(1/n)))^j*binomial(n+1, j)*Bernoulli(n+1-j).
%F A270103 T(n,k) = (1+k)*floor(k^(1/n)) - Sum_{j=1..floor(k^(1/n))} j^n. - _Daniel Hoying_, Jun 11 2020
%e A270103 The fifth entry in the second row of this array is 7, since 7 = floor(sqrt(1)) + floor(sqrt(2)) + floor(sqrt(3)) + floor(sqrt(4)) + floor(sqrt(5)).
%e A270103 The table array begins:
%e A270103 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
%e A270103 1, 2, 3, 5, 7, 9, 11, 13, 16, 19, ...
%e A270103 1, 2, 3, 4, 5, 6, 7, 9, 11, 13, ...
%e A270103 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...
%e A270103 ...
%t A270103 T[n_, k_] := (1 + k) Floor[k^(1/n)] - HarmonicNumber[Floor[k^(1/n)], -n] (* _Daniel Hoying_, Jun 11 2020 *)
%o A270103 (PARI) T(n, k) = sum(j=0, k, sqrtnint(j, n)); \\ _Michel Marcus_, Mar 12 2016
%Y A270103 Rows 1 to 5: A000217, A022554, A031876, A032512, A032513.
%Y A270103 Main diagonal and each diagonal below the main diagonal: A000027.
%K A270103 nonn,easy,tabl
%O A270103 1,2
%A A270103 _John M. Campbell_, Mar 11 2016