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 A143519 #41 Mar 18 2022 00:30:22
%S A143519 0,1,1,-1,1,-2,1,0,-1,-2,1,1,1,-2,-2,0,1,1,1,1,-2,-2,1,0,-1,-2,0,1,1,
%T A143519 3,1,0,-2,-2,-2,0,1,-2,-2,0,1,3,1,1,1,-2,1,0,-1,1,-2,1,1,0,-2,0,-2,-2,
%U A143519 1,-1,1,-2,1,0,-2,3,1,1,-2,3,1,0,1,-2,1,1,-2,3,1,0,0,-2,1,-1,-2,-2,-2,0,1
%N A143519 Moebius transform of A010051, the characteristic function of the primes: a(n) = Sum_{d|n} mu(n/d)*A010051(d); A054525 * A010051.
%C A143519 A010051 = A051731 * A143519 (since A051731 = the inverse Mobius transform).
%C A143519 A000720(n) = Sum_{k=1..n} a(k) floor(n/k) where A000720(n) is the number of primes <= n. - _Steven Foster Clark_, May 25 2018
%H A143519 Antti Karttunen, <a href="/A143519/b143519.txt">Table of n, a(n) for n = 1..10000</a>
%F A143519 Mobius transform of A010051, the characteristic function of the primes.
%F A143519 Row sums of triangle A143518.
%F A143519 a(n) = Sum_{d|n} A010051(d)*A008683(n/d). - _Antti Karttunen_, Jul 19 2017
%F A143519 a(n) = Sum_{a*b*c=n} omega(a)*mu(b)*mu(c). - _Benedict W. J. Irwin_, Mar 02 2022
%e A143519 a(4) = -1 since row 4 of triangle A043518 = (0, -1, 0, 0).
%e A143519 a(4) = -1 = (0, -1, 0, 1) dot (0, 1, 1, 0), where (0, -1, 0, 1) = row 4 of A054525 and A010051 = (0, 1, 1, 0, 1, 0, 1, 0, ...).
%t A143519 Table[Sum[MoebiusMu[n/d] Boole[PrimeQ@ d], {d, Divisors@ n}], {n, 89}] (* _Michael De Vlieger_, Jul 19 2017 *)
%o A143519 (Sage)
%o A143519 def A143519(n) :
%o A143519 D = filter(is_prime, divisors(n))
%o A143519 return add(moebius(n/d) for d in D)
%o A143519 [A143519(n) for n in (1..89)] # _Peter Luschny_, Feb 01 2012
%o A143519 (PARI) A143519(n) = sumdiv(n,d,isprime(d)*moebius(n/d)); \\ (After Luschny's Sage-code) - _Antti Karttunen_, Jul 19 2017
%Y A143519 Cf. A008683, A010051, A143518, A054525, A137851.
%K A143519 sign
%O A143519 1,6
%A A143519 _Gary W. Adamson_, Aug 22 2008
%E A143519 More terms from _R. J. Mathar_, Jan 19 2009