|
%I #8 Feb 21 2020 10:03:05
%S 1,1,2,3,3,4,5,6,5,7,8,9,8,9,10,13,11,12,13,14,13,16,17,18,15,17,18,
%T 21,20,21,22,23,20,23,24,27,25,26,27,30,27,28,29,30,29,34,35,36,31,33,
%U 34,37,36,37,38,41,38,41,42,43,40,41,42,47,43,46,47,48,47,50
%N a(n) = Sum_{k=1..n} (-1)^(k+1) * ceiling(n/k).
%F G.f.: (x/(1 - x)) * (1 + Sum_{k>=2} x^k / (1 + x^k)).
%F G.f.: (x/(1 - x)) * (1 + Sum_{k>=1} (-1)^(k+1) * x^(2*k) / (1 - x^k)).
%F a(n) = (n mod 2) + Sum_{k=1..n-1} A048272(k).
%t Table[Sum[(-1)^(k + 1) Ceiling[n/k], {k, 1, n}], {n, 1, 70}]
%t nmax = 70; CoefficientList[Series[(x/(1 - x)) (1 + Sum[x^k/(1 + x^k), {k, 2, nmax}]), {x, 0, nmax}], x] // Rest
%o (PARI) a(n) = sum(k=1, n, (-1)^(k+1)*ceil(n/k)); \\ _Michel Marcus_, Feb 21 2020
%Y Cf. A006590, A048272, A059851, A275495, A325937.
%K nonn
%O 1,3
%A _Ilya Gutkovskiy_, Feb 19 2020
|
