A324821 - OEIS

%I #12 Mar 19 2019 23:00:57

%S 0,3,7,5,15,10,31,8,11,19,63,21,127,46,30,16,255,27,511,44,63,78,1023,

%T 40,19,170,16,65,2047,38,4095,32,78,334,58,48,8191,766,236,64,16383,

%U 110,32767,177,49,1246,65535,80,35,51,260,341,131071,48,107,176,1004,2794,262143,104,524287,5454,80,64,142,219,1048575,641,1278,110

%N Xor-Moebius transform of A324819, where A324819(n) = bitor(2*A156552(n), A323243(n)), where bitor is A003986.

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

%H Antti Karttunen, <a href="/A324821/b324821.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(1+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 by _David A. Corneth_

%o A324819(n) = bitor(2*A156552(n),A323243(n)); \\ Needs code also from A323243.

%o A324821(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, A324819(d)))); (v); };

%Y Cf. A003986, A156552, A323243, A324815, A324819, A324820, A324876, A324878.

%K nonn

%O 1,2

%A _Antti Karttunen_, Mar 18 2019