A359824 - OEIS

%I #8 Jan 14 2023 18:36:46

%S 1,1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,1,1,1,

%T 1,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,1,1,0,0,

%U 1,1,0,0,0,1,0,0,1,1,0,0,0,1,0,1,1,1,1,1,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,1

%N Parity of A359823, where A359823 is the Dirichlet inverse of A359820.

%H Antti Karttunen, <a href="/A359824/b359824.txt">Table of n, a(n) for n = 1..100000</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%o (PARI)

%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o A359820(n) = ((n+A003415(n))%2);

%o memoA359823 = Map();

%o A359823(n) = if(1==n,1,my(v); if(mapisdefined(memoA359823,n,&v), v, v = -sumdiv(n,d,if(d<n,A359820(n/d)*A359823(d),0)); mapput(memoA359823,n,v); (v)));

%o A359824(n) = (A359823(n)%2);

%Y Characteristic function of A359825.

%Y Parity of A347082, A347084 and A359823.

%Y Cf. A359820, A359820.

%Y Cf. also A359764 [= a(A003961(n))].

%K nonn

%O 1

%A _Antti Karttunen_, Jan 14 2023