A333194 - OEIS

A333194

a(n) = Sum_{k=1..n} (ceiling(n/k) mod 2) * k.

1, 2, 4, 4, 8, 8, 11, 11, 19, 16, 21, 21, 30, 30, 37, 29, 45, 45, 51, 51, 66, 56, 67, 67, 88, 83, 96, 84, 105, 105, 112, 112, 144, 130, 147, 135, 159, 159, 178, 162, 197, 197, 208, 208, 241, 209, 232, 232, 277, 270, 290, 270, 309, 309, 324, 308, 357, 335, 364, 364

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..60.

FORMULA

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

a(n) = n*(n + 1)/2 - Sum_{k=1..n-1} A000593(k).

a(n) = A000217(n) - A078471(n-1).

MAPLE

b:= n-> add(d, d=select(x-> x::odd, numtheory[divisors](n))):

a:= proc(n) option remember; n+`if`(n<2, 0, a(n-1))-b(n-1) end: