A297110 Xor-Moebius transform of A006068, inverse of the binary Gray code.

1, 2, 3, 4, 7, 4, 4, 8, 12, 8, 12, 8, 8, 12, 15, 16, 31, 20, 28, 16, 31, 20, 27, 16, 23, 24, 28, 24, 23, 16, 20, 32, 48, 32, 63, 40, 56, 36, 48, 32, 48, 32, 51, 40, 48, 44, 52, 32, 36, 56, 63, 48, 39, 36, 47, 48, 48, 56, 44, 32, 40, 60, 63, 64, 112, 80, 124, 64, 96, 64, 123, 80, 112, 72, 111, 72, 127, 80, 116, 64

Offset: 1

Author

Antti Karttunen, Dec 25 2017

Keywords

• nonn
• base

Comments

Unique sequence satisfying SumXOR_{d divides n} a(d) = A006068(n) for all n > 0, where SumXOR is the analog of summation under the binary XOR operation. See A295901 for a list of some of the properties of the Xor-Moebius transform.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A006068, A256739, A295901, A296208.

Programs

PARI

A006068(n)= { my(s=1, ns); while(1, ns = n >> s; if(0==ns, break()); n = bitxor(n, ns); s <<= 1; ); return (n); } \\ Essentially Joerg Arndt's Jul 19 2012 code.
A297110(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, A006068(d)))); (v); };