A324712 - OEIS

%I #16 Mar 14 2019 17:51:56

%S 0,1,3,5,7,4,15,12,15,11,31,15,63,28,22,16,127,7,255,28,43,46,511,24,

%T 27,106,20,39,1023,60,2047,56,42,206,34,44,4095,508,172,32,8191,24,

%U 16383,113,57,734,32767,56,51,9,128,213,65535,4,67,116,748,1768,131071,26,262143,3406,20,72,70,125,524287,389,762,22

%N Xor-Moebius transform of A323243, where A323243(n) = sigma(A156552(n)).

%C Properties of Xor-Moebius transform are explained in A295901.

%H Antti Karttunen, <a href="/A324712/b324712.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) = A297106(n) XOR A324714(n).

%F a(A000040(n)) = A000225(n).

%o (PARI) A324712(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, A323243(d)))); (v); } \\ For A323243, see under that entry.

%Y Cf. A156552, A295901, A297106, A323243, A324543, A324713, A324714.

%K nonn

%O 1,3

%A _Antti Karttunen_, Mar 12 2019