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%I #9 Mar 31 2021 10:11:04

%S 1,0,-4,-8,-32,-32,-128,-256,-512,-512,-2048,-4096,-12288,-16384,

%T -16384,-32768,-131072,-262144,-786432,-1572864,-2097152,-2097152,

%U -8388608,-16777216,-33554432,-33554432,-67108864,-134217728,-536870912,-1610612736,-4294967296

%N A002321*A000079.

%C 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.

%C 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.

%F a(n) = 2^(n-1)*A002321(n). - _Chai Wah Wu_, Mar 30 2021

%o (Python)

%o from functools import lru_cache

%o @lru_cache(maxsize=None)

%o def A162459(n):

%o if n == 0:

%o return 0

%o c, j = n, 2

%o k1 = n//j

%o while k1 > 1:

%o j2 = n//k1 + 1

%o c += (j2-j)*A162459(k1)//2**(k1-1)

%o j, k1 = j2, n//j2

%o return 2**(n-1)*(j-c) # _Chai Wah Wu_, Mar 30 2021

%Y Cf. A002321, A000079.

%K sign

%O 1,3

%A _Mats Granvik_, Jul 04 2009