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 A382692 #22 Apr 22 2025 07:53:47
%S A382692 0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,
%T A382692 3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,
%U A382692 5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6
%N A382692 a(n) = floor of alternating sum of k-th roots of n, with k >= 2.
%F A382692 a(n) = floor(Sum_{k>=2} (-1)^k * n^(1/k)) = floor(Sum_{k>=1} (n^(1/(2*k)) - n^(1/(2*k + 1)))).
%F A382692 a(n) ~ A381042(n).
%F A382692 Series expansion of Sum_{k>=2} (-1)^k * x^(1/k) at x=1: Sum_{i>=0} A(i) * (x-1)^i/i!, where A(i) = KroneckerDelta(i, 1) - Sum_{j=1..i} eta(j) * StirlingS1(i, j), with eta as the Dirichlet eta function.
%e A382692 a(15) = floor(15^(1/2) - 15^(1/3) + 15^(1/4) - ...) = floor(1.9701...) = 1.
%t A382692 Floor@Table[NSum[n^(1/(2 k)) - n^(1/(2 k + 1)), {k, 1, Infinity}, WorkingPrecision -> 30], {n, 1, 100}]
%Y A382692 Cf. A000196 (k=2), A048766 (k=3), A255270 (k=4), A178487 (k=5), A178489 (k=6).
%Y A382692 Cf. A381042, A382691.
%K A382692 nonn
%O A382692 0,17
%A A382692 _Friedjof Tellkamp_, Apr 05 2025