A162459 A002321*A000079.

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

Author

Mats Granvik, Jul 04 2009

Keywords

• sign

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.

Crossrefs

Cf. A002321, A000079.

Programs

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

Formula

a(n) = 2^(n-1)*A002321(n). - Chai Wah Wu, Mar 30 2021