cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A162459 A002321*A000079.

This page as a plain text file.
%I A162459 #9 Mar 31 2021 10:11:04
%S A162459 1,0,-4,-8,-32,-32,-128,-256,-512,-512,-2048,-4096,-12288,-16384,
%T A162459 -16384,-32768,-131072,-262144,-786432,-1572864,-2097152,-2097152,
%U A162459 -8388608,-16777216,-33554432,-33554432,-67108864,-134217728,-536870912,-1610612736,-4294967296
%N A162459 A002321*A000079.
%C A162459 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 A162459 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 A162459 a(n) = 2^(n-1)*A002321(n). - _Chai Wah Wu_, Mar 30 2021
%o A162459 (Python)
%o A162459 from functools import lru_cache
%o A162459 @lru_cache(maxsize=None)
%o A162459 def A162459(n):
%o A162459     if n == 0:
%o A162459         return 0
%o A162459     c, j = n, 2
%o A162459     k1 = n//j
%o A162459     while k1 > 1:
%o A162459         j2 = n//k1 + 1
%o A162459         c += (j2-j)*A162459(k1)//2**(k1-1)
%o A162459         j, k1 = j2, n//j2
%o A162459     return 2**(n-1)*(j-c) # _Chai Wah Wu_, Mar 30 2021
%Y A162459 Cf. A002321, A000079.
%K A162459 sign
%O A162459 1,3
%A A162459 _Mats Granvik_, Jul 04 2009