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A324716 a(n) = 2*A156552(n) - bitand(2*A156552(n), A323243(n)), where bitand is bitwise-AND, A004198.

%I A324716 #9 Mar 15 2019 21:55:48
%S A324716 0,2,4,2,8,8,16,6,0,18,32,18,64,32,4,6,128,16,256,34,0,66,512,38,0,
%T A324716 130,4,70,1024,10,2048,30,64,258,0,22,4096,512,4,70,8192,72,16384,130,
%U A324716 8,1026,32768,78,0,32,256,258,65536,32,0,134,4,2048,131072,82,262144,4098,64,22,128,138,524288,518,1024,80,1048576,38,2097152,8194,20,1030,0,266
%N A324716 a(n) = 2*A156552(n) - bitand(2*A156552(n), A323243(n)), where bitand is bitwise-AND, A004198.
%C A324716 Equivalently, a(n) = 2*A156552(n) XOR (2*A156552(n) AND A323243(n)).
%H A324716 Antti Karttunen, <a href="/A324716/b324716.txt">Table of n, a(n) for n = 1..10000</a>
%H A324716 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A324716 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A324716 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%o A324716 (PARI)
%o A324716 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 A324716 A324716(n) = { my(t=2*A156552(n)); bitxor(t,bitand(t,A323243(n))); };
%o A324716 \\ Or equivalently:
%o A324716 A324716(n) = { my(t=2*A156552(n)); t - bitand(t,A323243(n)); };
%Y A324716 Cf. A003987, A004198, A156552, A323243, A324717, A324722 (positions of zeros).
%K A324716 nonn
%O A324716 1,2
%A A324716 _Antti Karttunen_, Mar 15 2019