A318503 Xor-Moebius transform of A001065, the sum of proper divisors.

0, 1, 1, 2, 1, 6, 1, 4, 5, 8, 1, 20, 1, 10, 9, 8, 1, 22, 1, 28, 11, 14, 1, 48, 7, 16, 9, 20, 1, 44, 1, 16, 15, 20, 13, 52, 1, 22, 17, 32, 1, 48, 1, 36, 45, 26, 1, 96, 9, 36, 21, 60, 1, 94, 17, 88, 23, 32, 1, 76, 1, 34, 39, 32, 19, 72, 1, 44, 27, 68, 1, 120, 1, 40, 63, 84, 19, 92, 1, 80, 37, 44, 1, 184, 23, 46, 33, 112, 1, 132

Offset

1,4

Comments

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

Formula

a(n) = A318501(n) XOR A318502(n).

Prog

(PARI) A318503(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, sigma(d)-d))); (v); } \\ after code in A295901.

Crossrefs

Cf. A001065, A051953, A256739, A295901, A296203, A318501, A318502.

Sequence in context: A048671 A335023 A205959 * A328580 A362784 A088123

Adjacent sequences: A318500 A318501 A318502 * A318504 A318505 A318506

Keyword

nonn

Author

Antti Karttunen, Aug 28 2018

Status

approved