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%I #8 Jan 10 2020 12:36:01
%S 0,1,2,0,1,2,2,1,0,0,1,2,2,2,1,0,1,1,2,1,0,0,1,2,0,2,2,2,2,0,1,1,1,0,
%T 2,0,2,2,0,0,1,1,2,1,1,0,1,2,0,1,1,2,2,2,0,2,0,2,1,1,2,0,2,0,2,0,1,1,
%U 1,2,2,1,1,2,2,2,1,1,2,1,0,0,1,0,0,2,0,0,2,0,0,1,1,0,2,2,1,1,1,0,2,0,1,2,0
%N a(n) = A156552(n) mod 3.
%H Antti Karttunen, <a href="/A329903/b329903.txt">Table of n, a(n) for n = 1..65537</a>
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F a(n) = A010872(A156552(n)) = A156552(n) mod 3.
%t Array[Mod[#, 3] &@ Floor@ Total@ Flatten@ MapIndexed[#1 2^(#2 - 1) &, Flatten[Table[2^(PrimePi@ #1 - 1), {#2}] & @@@ FactorInteger@ #]] &, 105] (* _Michael De Vlieger_, Dec 27 2019 *)
%o (PARI)
%o A156552(n) = {my(f = factor(n), p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
%o A329903(n) = (A156552(n)%3);
%Y Cf. A010872, A156552.
%Y Cf. A329609 (gives positions of zeros).
%K nonn
%O 1,3
%A _Antti Karttunen_, Dec 08 2019
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