A309124 a(n) = n - 3 * floor(n/3) + 5 * floor(n/5) - 7 * floor(n/7) + ...

1, 2, 0, 1, 7, 5, -1, 0, 7, 13, 3, 1, 15, 9, -3, -2, 16, 23, 5, 11, 23, 13, -9, -11, 20, 34, 14, 8, 38, 26, -4, -3, 17, 35, -1, 6, 44, 26, -2, 4, 46, 58, 16, 6, 48, 26, -20, -22, 21, 52, 16, 30, 84, 64, 4, -2, 34, 64, 6, -6, 56, 26, -16, -15, 69, 89, 23, 41, 85, 49, -21, -14, 60, 98, 36

Offset: 1

Author

Ilya Gutkovskiy, Jul 13 2019

Keywords

• sign

Comments

Partial sums of A050457.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A014200, A024919, A050457, A078471.

Programs

Maple

f:= proc(n) local r,d;
  r:= n/2^padic:-ordp(n,2);
  add((-1)^((d-1)/2)*d, d = numtheory:-divisors(r))
end proc:
ListTools:-PartialSums(map(f,[$1..100])); # Robert Israel, Oct 28 2020

Mathematica

Table[Sum[(-1)^(k + 1) (2 k - 1) Floor[n/(2 k - 1)], {k, 1, n}], {n, 1, 75}]
nmax = 75; CoefficientList[Series[1/(1 - x) Sum[(-1)^(k + 1) (2 k - 1) x^(2 k - 1)/(1 - x^(2 k - 1)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

Formula

G.f.: (1/(1 - x)) * Sum_{k>=1} (-1)^(k+1) * (2*k - 1) * x^(2*k-1)/(1 - x^(2*k-1)).