A324876 Xor-Moebius transform of A324866, where A324866(n) = A156552(n) OR (A323243(n) - A156552(n)).

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

Offset: 1

Author

Antti Karttunen, Mar 18 2019

Keywords

• nonn

Comments

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)).

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. A156552, A323243, A324820, A324821, A324866, A324877, 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
A318456(n) = bitor(n,sigma(n)-n);
A324866(n) = if(1==n,0,A318456(A156552(n)));
A324876(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, A324866(d)))); (v); };

Formula

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