cp's OEIS Frontend

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.

A345034 a(n) = Sum_{k=1..n} (-2)^(floor(n/k) - 1).

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%I A345034 #15 Jun 07 2021 09:10:00
%S A345034 1,-1,6,-8,17,-27,70,-136,255,-491,1046,-2082,4063,-8131,16476,-32882,
%T A345034 65423,-130845,262372,-524818,1048149,-2096045,4195412,-8390820,
%U A345034 16775029,-33550477,67113210,-134225588,268427597,-536854983,1073757754,-2147517076
%N A345034 a(n) = Sum_{k=1..n} (-2)^(floor(n/k) - 1).
%H A345034 Seiichi Manyama, <a href="/A345034/b345034.txt">Table of n, a(n) for n = 1..3000</a>
%F A345034 G.f.: (1/(1 - x)) * Sum_{k>=1} x^k * (1 - x^k)/(1 + 2*x^k).
%t A345034 a[n_] := Sum[(-2)^(Floor[n/k] - 1), {k, 1, n}]; Array[a, 30] (* _Amiram Eldar_, Jun 06 2021 *)
%o A345034 (PARI) a(n) = sum(k=1, n, (-2)^(n\k-1));
%o A345034 (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, x^k*(1-x^k)/(1+2*x^k))/(1-x))
%Y A345034 Column k=2 of A345033.
%Y A345034 Cf. A077925, A345028.
%K A345034 sign
%O A345034 1,3
%A A345034 _Seiichi Manyama_, Jun 06 2021