login
A162459
1
1, 0, -4, -8, -32, -32, -128, -256, -512, -512, -2048, -4096, -12288, -16384, -16384, -32768, -131072, -262144, -786432, -1572864, -2097152, -2097152, -8388608, -16777216, -33554432, -33554432, -67108864, -134217728, -536870912, -1610612736, -4294967296
OFFSET
1,3
COMMENTS
Appears to be the determinant of n X n (-1,1) matrix defined by A(i,j)=1 if j=1 or i divides j else -1.
Appears also to be the determinant of n X n (-i/j,i/j) matrix defined by A(i,j)=i/j if j=1 or i divides j else -i/j.
FORMULA
a(n) = 2^(n-1)*A002321(n). - Chai Wah Wu, Mar 30 2021
PROG
(Python)
from functools import lru_cache
@lru_cache(maxsize=None)
def A162459(n):
if n == 0:
return 0
c, j = n, 2
k1 = n//j
while k1 > 1:
j2 = n//k1 + 1
c += (j2-j)*A162459(k1)//2**(k1-1)
j, k1 = j2, n//j2
return 2**(n-1)*(j-c) # Chai Wah Wu, Mar 30 2021
CROSSREFS
Sequence in context: A149092 A188117 A094502 * A129195 A180098 A124143
KEYWORD
sign
AUTHOR
Mats Granvik, Jul 04 2009
STATUS
approved