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 A378228 #8 Nov 24 2024 09:29:25
%S A378228 1,-8,-18,12,-40,144,-84,0,45,320,-154,-216,-234,672,720,0,-340,-360,
%T A378228 -456,-480,1512,1232,-690,0,175,1872,0,-1008,-928,-5760,-1178,0,2772,
%U A378228 2720,3360,540,-1554,3648,4212,0,-1804,-12096,-2064,-1848,-1800,5520,-2538,0,539,-1400,6120,-2808,-3180,0,6160,0,8208,7424
%N A378228 Dirichlet inverse of A341528, where A341528(n) = n * sigma(A003961(n)), and A003961 is fully multiplicative with a(prime(i)) = prime(i+1).
%C A378228 Multiplicative because A341528 is.
%H A378228 Antti Karttunen, <a href="/A378228/b378228.txt">Table of n, a(n) for n = 1..20000</a>
%H A378228 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>.
%H A378228 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.
%F A378228 a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A341528(n/d) * a(d).
%o A378228 (PARI)
%o A378228 A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
%o A378228 A341528(n) = (n*sigma(A003961(n)));
%o A378228 memoA378228 = Map();
%o A378228 A378228(n) = if(1==n,1,my(v); if(mapisdefined(memoA378228,n,&v), v, v = -sumdiv(n,d,if(d<n,A341528(n/d)*A378228(d),0)); mapput(memoA378228,n,v); (v)));
%Y A378228 Dirichlet inverse of A341528.
%Y A378228 Cf. A003973, A378221.
%Y A378228 Cf. also A378229.
%K A378228 sign,mult
%O A378228 1,2
%A A378228 _Antti Karttunen_, Nov 23 2024