A324712 Xor-Moebius transform of A323243, where A323243(n) = sigma(A156552(n)).

0, 1, 3, 5, 7, 4, 15, 12, 15, 11, 31, 15, 63, 28, 22, 16, 127, 7, 255, 28, 43, 46, 511, 24, 27, 106, 20, 39, 1023, 60, 2047, 56, 42, 206, 34, 44, 4095, 508, 172, 32, 8191, 24, 16383, 113, 57, 734, 32767, 56, 51, 9, 128, 213, 65535, 4, 67, 116, 748, 1768, 131071, 26, 262143, 3406, 20, 72, 70, 125, 524287, 389, 762, 22

Offset: 1

Author

Antti Karttunen, Mar 12 2019

Keywords

• nonn

Comments

Properties of Xor-Moebius transform are explained in A295901.

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, A295901, A297106, A323243, A324543, A324713, A324714.

Programs

PARI

A324712(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, A323243(d)))); (v); } \\ For A323243, see under that entry.

Formula

a(n) = A297106(n) XOR A324714(n).

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