A359774 - OEIS

%I #14 Jan 16 2023 21:55:26

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

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

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

%N Parity of A359773, where A359773 is the Dirichlet inverse of A356163.

%H Antti Karttunen, <a href="/A359774/b359774.txt">Table of n, a(n) for n = 1..100000</a>

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

%F a(n) = A359773(n) mod 2.

%F a(n) <= A356163(n). [See comments in A359773]

%o (PARI)

%o A356163(n) = (1-(((n=factor(n))[, 1]~*n[, 2])%2)); \\ After code in A001414.

%o memoA359773 = Map();

%o A359773(n) = if(1==n,1,my(v); if(mapisdefined(memoA359773,n,&v), v, v = -sumdiv(n,d,if(d<n,A356163(n/d)*A359773(d),0)); mapput(memoA359773,n,v); (v)));

%o A359774(n) = (A359773(n)%2);

%Y Characteristic function of A359775, whose complement A359776 gives the positions of 0's.

%Y Parity of A359773 and of A359789.

%Y Cf. A001414, A359773, A359777 (where differs from A356163).

%Y Cf. also A359764 [= a(A003961(n))], A359787.

%K nonn

%O 1

%A _Antti Karttunen_, Jan 13 2023