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%I #15 Mar 14 2019 17:52:04
%S 0,3,7,2,15,12,31,6,0,31,63,26,127,48,6,6,255,20,511,50,3,114,1023,54,
%T 4,214,4,118,2047,10,4095,30,114,434,2,30,8191,768,20,118,16383,108,
%U 32767,194,8,1826,65535,110,12,45,504,386,131071,36,19,198,20,3348,262143,122,524287,6834,112,22,246,234,1048575,822,1794,120
%N a(n) = 2*A156552(n) XOR A323243(n).
%C a(n) is also the cumulative XOR of (2*A297106(d) XOR A324712(d)) over the divisors d of n.
%C It is conjectured that a(n) may obtain value zero only when n is a power of prime, and especially for n > 1, it must be a prime power present in A324201.
%H Antti Karttunen, <a href="/A324713/b324713.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) XOR A323243(n).
%F a(n) = XORsum_{d|n} (2*A297106(d) XOR A324712(d)).
%o (PARI) A324713(n) = { my(x=0,s=0); fordiv(n,d,x = bitxor(x,A324712(d)); s = bitxor(s,A297106(d))); bitxor(x,2*s); };
%Y Cf. A003987, A156552, A297106, A323243, A323244, A324201, A324712, A324714.
%K nonn
%O 1,2
%A _Antti Karttunen_, Mar 13 2019
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