A378227 XOR-Moebius transform of A318467, where A318467(n) = 2*n XOR sigma(n).

3, 4, 1, 8, 15, 6, 5, 16, 29, 14, 25, 12, 23, 6, 11, 32, 51, 30, 49, 12, 13, 22, 53, 24, 33, 14, 1, 12, 39, 126, 29, 64, 105, 70, 127, 20, 111, 70, 99, 24, 123, 58, 121, 12, 15, 38, 109, 48, 93, 30, 31, 28, 95, 22, 51, 24, 17, 14, 73, 172, 71, 6, 1, 128, 205, 114, 193, 140, 221, 102, 197, 72, 219, 142, 205, 108

Offset: 1

Author

Antti Karttunen, Nov 26 2024

Keywords

• nonn

Comments

Unique sequence satisfying SumXOR_{d divides n} a(d) = A318467(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..65537
• Index entries for sequences related to binary expansion of n
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A003987, A256739, A296203, A318467.

Cf. also A083254, A378226.

Programs

PARI

A318467(n) = bitxor(2*n, sigma(n));
A378227(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, A318467(d)))); (v); }

Formula

a(n) = 2*A256739(n) XOR A296203(n).