cp's OEIS Frontend

A350239 a(n) = Sum_{k=1..n} (-1)^(k+1) * floor((n/(2*k))^k).

%I A350239 #16 Dec 22 2021 07:09:05
%S A350239 0,1,1,1,1,2,1,1,1,2,2,1,2,2,1,0,0,2,2,2,2,3,1,0,1,3,2,2,1,4,-1,-1,2,
%T A350239 2,2,1,2,1,1,0,2,3,1,2,0,2,0,-2,1,2,2,-1,2,2,-2,2,1,2,2,-1,0,3,3,-1,
%U A350239 -1,7,2,2,1,2,0,0,-2,3,1,2,-2,4,-3,-2,-2,3,1,-1,0,1,2,1,1,0,2,3,1,5,2,-1,2,4,1,1,0,1,1
%N A350239 a(n) = Sum_{k=1..n} (-1)^(k+1) * floor((n/(2*k))^k).
%H A350239 Seiichi Manyama, <a href="/A350239/b350239.txt">Table of n, a(n) for n = 1..5000</a>
%e A350239 a(3) = [3/2]  = 1.
%e A350239 a(4) = [4/2] - [(4/4)^2] = 2 - 1 = 1.
%e A350239 a(5) = [5/2] - [(5/4)^2] = 2 - 1 = 1.
%t A350239 a[n_] := Sum[(-1)^(k + 1)*Floor[(n/(2*k))^k], {k, 1, n}]; Array[a, 100] (* _Amiram Eldar_, Dec 21 2021 *)
%o A350239 (PARI) a(n) = sum(k=1, n\2, (-1)^(k+1)*(n^k\(2*k)^k));
%Y A350239 Cf. A350223, A350238.
%K A350239 sign
%O A350239 1,6
%A A350239 _Seiichi Manyama_, Dec 21 2021