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

1,1

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)

Formula

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

Prog

(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); }

Crossrefs

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

Cf. also A083254, A378226.

Sequence in context: A326503 A378913 A105578 * A198739 A158076 A010611

Adjacent sequences: A378224 A378225 A378226 * A378228 A378229 A378230

Keyword

nonn

Author

Antti Karttunen, Nov 26 2024

Status

approved