A378226 XOR-Moebius transform of A318457, where A318457(n) = n XOR (sigma(n)-n).

1, 2, 3, 4, 5, 0, 7, 8, 15, 4, 11, 24, 13, 0, 1, 16, 17, 8, 19, 4, 27, 16, 23, 40, 27, 4, 27, 0, 29, 52, 31, 32, 39, 36, 45, 8, 37, 32, 57, 16, 41, 0, 43, 24, 5, 32, 47, 80, 63, 0, 53, 20, 53, 104, 41, 112, 63, 4, 59, 124, 61, 0, 7, 64, 91, 48, 67, 76, 75, 36, 71, 0, 73, 68, 103, 56, 83, 36, 79, 48, 111, 84, 83

Offset

1,2

Comments

Unique sequence satisfying SumXOR_{d divides n} a(d) = A318457(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)

Prog

(PARI)
A318457(n) = bitxor(n, sigma(n)-n);
A378226(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, A318457(d)))); (v); }

Crossrefs

Cf. A000203, A001065, A003987, A318457, A378227, A378230 (positions of 0's), A378441 (fixed points).

Sequence in context: A126441 A004181 A080744 * A265518 A256296 A256306

Adjacent sequences: A378223 A378224 A378225 * A378227 A378228 A378229

Keyword

nonn

Author

Antti Karttunen, Nov 26 2024

Status

approved