A296207 Xor-Moebius transform of A227320, binary XOR of proper divisors of n.

0, 1, 1, 2, 1, 0, 1, 4, 3, 6, 1, 0, 1, 4, 7, 8, 1, 12, 1, 12, 5, 8, 1, 0, 5, 14, 9, 8, 1, 6, 1, 16, 9, 18, 3, 24, 1, 16, 15, 24, 1, 26, 1, 16, 5, 20, 1, 0, 7, 22, 19, 28, 1, 0, 15, 16, 17, 30, 1, 12, 1, 28, 31, 32, 9, 58, 1, 36, 21, 38, 1, 48, 1, 38, 19, 32, 13, 54, 1, 48, 27, 42, 1, 52, 21, 40, 31, 32, 1, 34, 11, 40, 29, 44, 23, 0, 1

Offset: 1

Author

Antti Karttunen, Dec 25 2017

Keywords

• nonn
• base

Comments

Unique sequence satisfying SumXOR_{d divides n} a(d) = A227320(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 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. A003987, A178910, A227320, A256739, A295901, A296206.

Cf. A297107 (positions of zeros).

Programs

PARI

A227320(n) = { my(s=0); fordiv(n,d,if(dA296207(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, A227320(d)))); (v); } \\ after code in A295901.

Formula

a(n) = n XOR A256739(n), where XOR is the bitwise XOR-operation (A003987).