cp's OEIS Frontend

A324867 a(n) = A156552(n) XOR A324865(n), where XOR is bitwise-xor, A003987.

%I A324867 #8 Mar 18 2019 21:49:45
%S A324867 0,1,3,2,7,4,15,6,0,13,31,10,63,16,2,6,127,12,255,18,7,46,511,22,28,
%T A324867 82,4,46,1023,30,2047,30,54,174,2,22,4095,256,12,54,8191,36,16383,66,
%U A324867 24,798,32767,46,60,31,248,130,65535,28,19,70,12,1300,131071,42,262143,2734,48,22,126,94,524287,302,774,40,1048575,38,2097151,4354,10
%N A324867 a(n) = A156552(n) XOR A324865(n), where XOR is bitwise-xor, A003987.
%H A324867 Antti Karttunen, <a href="/A324867/b324867.txt">Table of n, a(n) for n = 1..10000</a> (based on Hans Havermann's factorization of A156552)
%H A324867 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A324867 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A324867 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A324867 a(1) = 0; for n > 1, a(n) = A318457(A156552(n)).
%F A324867 a(n) = A156552(n) XOR (A323243(n) - A156552(n)).
%F A324867 a(n) = A323243(n) - 2*A324398(n).
%o A324867 (PARI)
%o A324867 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 A324867 A318457(n) = bitxor(n,sigma(n)-n);
%o A324867 A324867(n) = if(1==n,0,A318457(A156552(n)));
%o A324867 (PARI) A324867(n) = { my(k=A156552(n)); bitxor(k,(A323243(n)-k)); }; \\ Needs also code from A323243.
%Y A324867 Cf. A001065, A003986, A156552, A318457, A323243, A324865, A324866, A324398, A324877.
%K A324867 nonn
%O A324867 1,3
%A A324867 _Antti Karttunen_, Mar 18 2019