A324821 Xor-Moebius transform of A324819, where A324819(n) = bitor(2*A156552(n), A323243(n)), where bitor is A003986.

0, 3, 7, 5, 15, 10, 31, 8, 11, 19, 63, 21, 127, 46, 30, 16, 255, 27, 511, 44, 63, 78, 1023, 40, 19, 170, 16, 65, 2047, 38, 4095, 32, 78, 334, 58, 48, 8191, 766, 236, 64, 16383, 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

Offset: 1

Author

Antti Karttunen, Mar 18 2019

Keywords

• nonn

Comments

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)).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000 (based on Hans Havermann's factorization of A156552)
• Index entries for sequences related to binary expansion of n
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

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

Programs

PARI

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
A324819(n) = bitor(2*A156552(n),A323243(n)); \\ Needs code also from A323243.
A324821(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, A324819(d)))); (v); };

Formula

a(A000040(n)) = A000225(1+n).