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.
%I A140254 #6 Feb 16 2025 08:33:08 %S A140254 1,1,2,0,4,-3,6,0,0,-5,10,0,12,-7,-6,0,16,0,18,0,-8,-11,22,0,0,-13,0, %T A140254 0,28,7,30,0,-12,-17,-10,0,36,-19,-14,0,40,9,42,0,0,-23,46,0,0,0,-18, %U A140254 0,52,0,-14,0,-20,-29,58,0,60,-31,0,0,-16,13,66,0,-24,11,70,0,72,-37,0,0,-16 %N A140254 Mobius transform of A014963. %C A140254 Conjectures relating to the Mobius sequence A008683: %C A140254 If mu(n) = 0, a(n) = 0. %C A140254 If mu(n) = 1, (n>1), a(n) = a negative term. %C A140254 If mu(n) = -1, a(n) = a positive term. %C A140254 So except for the first term and zero divided by zero we would have mu(n) = -a(n)/abs(a(n)). %C A140254 Examples: mu(4) = 0, a(4) = 0; mu(6) = 1, a(6) = (-3); mu(7) = (-1), a(7) = 6. %H A140254 Physics Forums discussion, <a href="http://www.physicsforums.com/showthread.php?t=35060">Moebius function</a>. %H A140254 Eric. W. Weisstein, <a href="https://mathworld.wolfram.com/MertensConjecture.html">Mertens Conjecture</a>. %F A140254 A054525 as an infinite lower triangular matrix * A014963 as a vector. %e A140254 a(5) = -3 = (1, -1, -1, 0, 0, 1) dot (1, 2, 3, 2, 5, 1) = (1 - 2 - 3 + 0 + 0 + 1), where (1, -1, -1, 0, 0, 1) = row 5 of triangle A054525 and (1, 2, 3, 2, 5, 1) = the first 5 terms of A014963. %Y A140254 Cf. A014963, A008683, A140255, A140256. %K A140254 sign %O A140254 1,3 %A A140254 _Gary W. Adamson_ and _Mats Granvik_, May 16 2008, Jun 29 2008 %E A140254 More terms from _Mats Granvik_, Jun 29 2008