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 A359433 #17 Jan 04 2023 02:09:47 %S A359433 1,-1,-1,-1,-1,1,-1,1,-2,1,-1,1,-1,1,1,1,-1,2,-1,1,1,1,-1,-1,-4,1,2,1, %T A359433 -1,-1,-1,-1,1,1,1,2,-1,1,1,-1,-1,-1,-1,1,2,1,-1,-1,-6,4,1,1,-1,-2,1, %U A359433 -1,1,1,-1,-1,-1,1,2,-1,1,-1,-1,1,1,-1,-1,-2,-1,1,4,1,1,-1,-1,-1,4,1,-1,-1,1,1,1,-1,-1,-2,1,1,1,1,1,1,-1,6,2,4,-1,-1,-1,-1,-1 %N A359433 Dirichlet inverse of A071773. %C A359433 Multiplicative because A071773 is. %H A359433 Antti Karttunen, <a href="/A359433/b359433.txt">Table of n, a(n) for n = 1..65537</a> %F A359433 Multiplicative with a(p^e) = (-1)^e * (1-p)^floor(e/2). - _Sebastian Karlsson_, Jan 03 2023 %t A359433 f[p_, e_] := (-1)^e * (1-p)^Floor[e/2]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Jan 04 2023 *) %o A359433 (PARI) %o A359433 A071773(n) = { my(f=factor(n)); prod(i=1, #f~, f[i, 1]^(f[i, 2]>1)); }; %o A359433 memoA359433 = Map(); %o A359433 A359433(n) = if(1==n,1,my(v); if(mapisdefined(memoA359433,n,&v), v, v = -sumdiv(n,d,if(d<n,A071773(n/d)*A359433(d),0)); mapput(memoA359433,n,v); (v))); %Y A359433 Cf. A071773. %Y A359433 Cf. A038838 (positions of even terms), A122132 (of odd terms), A353627 (parity of terms). %Y A359433 Cf. also A359432. %K A359433 sign,mult %O A359433 1,9 %A A359433 _Antti Karttunen_, Jan 02 2023