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

1,2

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

Prog

(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); };

Crossrefs

Cf. A006068, A256739, A295901, A296208.

Sequence in context: A072717 A139072 A021430 * A267695 A138676 A297111

Adjacent sequences: A297107 A297108 A297109 * A297111 A297112 A297113

Keyword

nonn,base

Author

Antti Karttunen, Dec 25 2017

Status

approved