OFFSET
0,2
LINKS
Chai Wah Wu, Table of n, a(n) for n = 0..53 (terms n = 0..32 from Karl-Heinz Hofmann)
FORMULA
EXAMPLE
For n=3, the size of the division cube matrix is 8 X 8 X 8:
.
: : : : : : : : :
.
z = 4 | 1 2 3 4 5 6 7 8
------+----------------------
1 /| o o o o o o o o 8
2 / | o . o . o . o . 4 64 Sum (z = 1)
3/ | o o o o o o o o 8 /
/ o . 4 48 Sum (z = 2)
z = 5 |/1 2 3 4 5 6 7 8 o 8 /
------+---------------------- 4 60 Sum (z = 3)
1 /| o o o o o o o o 8 8 /
2 / | o o o o o o o o 8 4 /
3/ | o o o o o o o o 8 --/
/ o o 8 48 Sum (z = 4)
z = 6 |/1 2 3 4 5 6 7 8 o 7 /
------+---------------------- 8 /
1 /| o o o o o o o o 8 8 /
2 / | o . o . o . o . 4 8 /
3/ | o o o o o o o o 6 --/
/ o . 4 63 Sum (z = 5)
z = 7 |/1 2 3 4 5 6 7 8 o 8 /
------+---------------------- 3 /
1 /| o o o o o o o o 8 8 /
2 / | o o o o o o o o 8 4 /
3/ | o o o o o o o o 8 --/
/ o o 8 45 Sum (z = 6)
z = 8 |/1 2 3 4 5 6 7 8 o 8 /
------+---------------------- 8 /
1 | o o o o o o o o 8 7 /
2 | o . o . o . o . 4 8 /
3 | o o o o o o o o 8 --/
4 | o . o . o . o . 4 63 Sum (z = 7)
5 | o o o o o o o o 8 /
6 | o . o . o . o . 4 /
7 | o o o o o o o o 8 /
8 | o . o . o . o . 4 /
--/
48 Sum (z = 8)
|
---
439 Cube Sum (z = 1..8)
MATHEMATICA
Array[Sum[MoebiusMu[k]*Floor[(2^#)/k]^3, {k, 2^# + 1}] &, 22, 0] (* Michael De Vlieger, Apr 05 2021 *)
PROG
(Python)
from labmath import mobius
def A342935(n): return sum(mobius(k)*(2**n//k)**3 for k in range(1, 2**n+1))
CROSSREFS
KEYWORD
nonn
AUTHOR
Karl-Heinz Hofmann, Mar 29 2021
EXTENSIONS
Edited by N. J. A. Sloane, Jun 13 2021
STATUS
approved