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 A378643 #14 Dec 03 2024 19:49:55
%S A378643 1,-1,-2,0,-4,4,-6,0,-1,6,-10,-2,-12,8,10,0,-16,-3,-18,0,14,12,-22,0,
%T A378643 -3,14,-2,2,-28,-28,-30,0,22,18,26,8,-36,20,26,-2,-40,-36,-42,2,4,24,
%U A378643 -46,0,-5,-1,34,2,-52,4,42,-4,38,30,-58,18,-60,32,6,0,50,-52,-66,2,46,-44,-70,-4,-72,38,2,2,62,-60,-78,0
%N A378643 Dirichlet inverse of A103977.
%H A378643 Antti Karttunen, <a href="/A378643/b378643.txt">Table of n, a(n) for n = 1..20000</a>
%F A378643 a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A103977(n/d) * a(d).
%F A378643 a(n) = A323910(n) when n is a non-abundant number (A263837), and also for some of the abundant numbers, A005101.
%o A378643 (PARI)
%o A378643 memoA378643 = Map();
%o A378643 A378643(n) = if(1==n,1,my(v); if(mapisdefined(memoA378643,n,&v), v, v = -sumdiv(n,d,if(d<n,A103977(n/d)*A378643(d),0)); mapput(memoA378643,n,v); (v)));
%Y A378643 Dirichlet inverse of A103977.
%Y A378643 Cf. A005101, A263837, A323910, A378645, A378646, A378647.
%K A378643 sign
%O A378643 1,3
%A A378643 _Antti Karttunen_, Dec 03 2024