|
|
A333194
|
|
a(n) = Sum_{k=1..n} (ceiling(n/k) mod 2) * k.
|
|
1
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
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).
|
|
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:
|
|
MATHEMATICA
|
Table[Sum[Mod[Ceiling[n/k], 2] k, {k, 1, n}], {n, 1, 60}]
Table[n (n + 1)/2 - Sum[DivisorSum[k, (-1)^(k/# + 1) # &], {k, 1, n - 1}], {n, 1, 60}]
nmax = 60; CoefficientList[Series[x/(1 - x) (1/(1 - x)^2 - Sum[k x^k/(1 + x^k), {k, 1, nmax}]), {x, 0, nmax}], x] // Rest
|
|
PROG
|
(PARI) a(n) = sum(k=1, n, (ceil(n/k) % 2)*k); \\ Michel Marcus, May 26 2020
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|