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 A354825 #8 Jun 09 2022 11:41:32
%S A354825 1,-2,-2,1,-2,4,-2,-2,1,4,-2,-2,-2,4,4,8,-2,-2,-2,-2,4,4,-2,4,1,4,-2,
%T A354825 -2,-2,-8,-2,-16,4,4,4,1,-2,4,4,4,-2,-8,-2,-2,-2,4,-2,-16,1,-2,4,-2,
%U A354825 -2,4,4,4,4,4,-2,4,-2,4,-2,20,4,-8,-2,-2,4,-8,-2,-2,-2,4,-2,-2,4,-8,-2,-16,8,4,-2,4,4,4,4,4
%N A354825 Dirichlet inverse of A293442, where A293442 is multiplicative with a(p^e) = A019565(e).
%C A354825 Multiplicative because A293442 is.
%H A354825 Antti Karttunen, <a href="/A354825/b354825.txt">Table of n, a(n) for n = 1..16384</a>
%H A354825 Antti Karttunen, <a href="/A354825/a354825.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F A354825 a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A293442(n/d) * a(d).
%o A354825 (PARI)
%o A354825 A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
%o A354825 A293442(n) = factorback(apply(e -> A019565(e),factor(n)[,2]));
%o A354825 memoA354825 = Map();
%o A354825 A354825(n) = if(1==n,1,my(v); if(mapisdefined(memoA354825,n,&v), v, v = -sumdiv(n,d,if(d<n,A293442(n/d)*A354825(d),0)); mapput(memoA354825,n,v); (v)));
%Y A354825 Cf. A019565, A293442.
%K A354825 sign,mult
%O A354825 1,2
%A A354825 _Antti Karttunen_, Jun 09 2022