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%I #13 Mar 28 2019 20:23:54
%S 0,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,
%T 0,1,0,1,1,1,0,1,0,1,1,1,0,1,0,0,1,1,0,1,0,1,1,1,0,1,0,1,1,1,0,1,0,1,
%U 0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,1
%N a(n) = 1 if A055396(n) < A324885(n), otherwise 0.
%C Difference between the 2-adic valuations of A324819(n) and A324866(n).
%C Of the first 10000 terms, 2540 are 0's and 7460's are 1's. Even n such that a(n) = 0 are rare: 2, 10, 50, 98, 154, 266, 374, 598, 770, 1054, 1250, 1558, 2162, 2662, 3422, 4154, 5390, 5402, 6578, 6806, 8342, 8918, 9682 are all such n less than 10001.
%H Antti Karttunen, <a href="/A324883/b324883.txt">Table of n, a(n) for n = 1..10000</a> (based on Hans Havermann's factorization of A156552)
%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>
%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F a(n) = A324884(n) - A324882(n).
%F For n > 1, a(n) = A007814(A324819(n)) - A007814(A324866(n)).
%F For n > 1, a(n) = A324903(A156552(n)).
%F a(p) = 0 for all primes p.
%o (PARI)
%o \\ Needs code also from A323243.
%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 A324819(n) = bitor(2*A156552(n),A323243(n));
%o A324866(n) = { my(k=A156552(n)); bitor(k,(A323243(n)-k)); };
%o A001511ext(n) = if(!n,n,sign(n)*(1+valuation(n,2))); \\ Like A001511 but gives 0 for 0 and -A001511(-n) for negative numbers.
%o A324882(n) = A001511ext(A324866(n));
%o A324884(n) = A001511ext(A324819(n));
%o A324883(n) = (A324884(n)-A324882(n));
%Y Cf. A001511, A007814, A055396, A156552, A323243, A324819, A324866, A324882, A324884, A324885, A324903.
%K nonn
%O 1
%A _Antti Karttunen_, Mar 28 2019
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