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%I #10 Mar 17 2019 21:08:22
%S 0,0,0,4,0,2,0,8,12,0,0,4,0,2,16,24,0,10,0,4,36,0,0,8,24,0,24,0,0,32,
%T 0,32,4,0,40,32,0,2,128,8,0,2,0,4,36,0,0,16,48,18,4,4,0,26,72,8,512,2,
%U 0,4,0,0,12,104,8,0,0,0,4,2,0,72,0,0,32,0,80,0,0,16,8,0,0,20,256,0,2048,0,0,74,128,0,0,0,520,56,0,32,128,64,0,2,0,8,64
%N a(n) = 2*A156552(n) AND A323243(n), where AND is bitwise-and, A004198.
%H Antti Karttunen, <a href="/A324815/b324815.txt">Table of n, a(n) for n = 1..10000</a> (based on Hans Havermann's factorization of A156552)
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</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) = 2*A156552(n) AND A323243(n), where AND is A004198.
%F a(n) = 2*A156552(n) - A324716(n) = 2*A156552(n) XOR A324716(n), where XOR is A003987.
%F For n > 1, a(n) = A318468(A156552(n)).
%F a(p) = 0 for all primes p.
%F a(A324201(n)) = A139256(n).
%F A000120(a(n)) = A324816(n).
%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 by _David A. Corneth_
%o A324815(n) = bitand(2*A156552(n),A323243(n)); \\ Needs code also from A323243.
%Y Cf. A003987, A004198, A139256, A156552, A318468, A323243, A324201, A324716, A324816.
%K nonn
%O 1,4
%A _Antti Karttunen_, Mar 17 2019
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