A324876 - OEIS

%I #9 Mar 19 2019 23:01:17

%S 0,1,3,2,7,7,15,4,5,11,31,12,63,31,14,8,127,13,255,28,27,49,511,24,27,

%T 109,8,60,1023,24,2047,16,42,209,30,28,4095,511,114,32,8191,43,16383,

%U 110,17,737,32767,48,51,9,134,210,65535,24,47,108,498,1771,131071,38,262143,3409,36,32,70,94,524287,386,762,42,1048575,52,2097151,7933,11

%N Xor-Moebius transform of A324866, where A324866(n) = A156552(n) OR (A323243(n) - A156552(n)).

%C It seems that the records, which are A000225(n) = 2^n - 1 occur at primes, as occur also the records for the width of terms, A000523(a(n)), and the records for the binary weights of terms, A000120(a(n)).

%H Antti Karttunen, <a href="/A324876/b324876.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(A000040(n)) = A000225(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

%o A318456(n) = bitor(n,sigma(n)-n);

%o A324866(n) = if(1==n,0,A318456(A156552(n)));

%o A324876(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, A324866(d)))); (v); };

%Y Cf. A156552, A323243, A324820, A324821, A324866, A324877, A324878.

%K nonn

%O 1,3

%A _Antti Karttunen_, Mar 18 2019