A353380 - OEIS

%I #12 Apr 19 2022 17:34:36

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

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

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

%N a(n) = 1 if A353354(n) [= Sum_{d|n} A332823(d)] is zero, otherwise 0.

%H Antti Karttunen, <a href="/A353380/b353380.txt">Table of n, a(n) for n = 1..65537</a>

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

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%F a(n) = [A353328(n) = A353329(n)], where [ ] is the Iverson bracket, giving 1 only if A353328(n) and A353329(n) are equal, and 0 otherwise.

%F a(p) = 0 for all primes p.

%F a(n) = a(A003961(n)) = a(A348717(n)), for all n >= 1.

%o (PARI)

%o A332823(n) = { my(f = factor(n),u=(sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2)%3); if(2==u,-1,u); };

%o A353354(n) = sumdiv(n,d,A332823(d));

%o A353380(n) = (0==A353354(n));

%Y Characteristic function of A353355.

%Y Cf. A048675, A332823, A353328, A353329, A353354, A353381, A353382 (inverse Möbius transform), A353414.

%K nonn

%O 1

%A _Antti Karttunen_, Apr 16 2022