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 A130030 #5 Mar 22 2020 17:10:55
%S A130030 2,1,1,2,3,6,5,7,9,14,11,15,17,20,21,22,27,20,31,23,33,38,39,20,45,48,
%T A130030 43,35,53,6,67,47,65,64,63,25,85,78,73,34,99,20,107,63,45,94,119,35,
%U A130030 113,56,99,73,137,54,103,54,117,134,161,-1,163,136,73,96,113,24,199,107,159,12,213
%N A130030 a(n) = Sum_{d|n} (-1)^omega(n/d) * phi(rad(n/d)) * prime(d).
%C A130030 Old name: A129691 * A000040.
%C A130030 A130029 = A054523 * A000040.
%F A130030 A129691 as an infinite lower triangular matrix * A000040, the primes.
%F A130030 From _Ilya Gutkovskiy_, Mar 22 2020: (Start)
%F A130030 a(n) = Sum_{d|n} A023900(n/d) * prime(d).
%F A130030 Sum_{k=1..n} a(gcd(n,k)) = prime(n). (End)
%e A130030 a(4) = 2 = dot product of row 4 of A129691: (-1, -1, 0, 1) and the first four primes: (2, 3, 5, 7) = (-2, -3, 0, 7) = 2.
%Y A130030 Cf. A000010, A000040, A001221, A007444, A007947, A023900, A054523, A076479, A129691, A130029, A333177.
%K A130030 sign
%O A130030 1,1
%A A130030 _Gary W. Adamson_, May 02 2007
%E A130030 New name and more terms from _Ilya Gutkovskiy_, Mar 22 2020