A296203 Xor-Moebius transform of A000203, the sum of divisors.

1, 2, 5, 4, 7, 10, 9, 8, 9, 22, 13, 20, 15, 18, 27, 16, 19, 34, 21, 60, 45, 42, 25, 40, 25, 38, 37, 36, 31, 78, 33, 32, 57, 38, 63, 108, 39, 42, 51, 120, 43, 90, 45, 116, 95, 82, 49, 80, 49, 86, 95, 76, 55, 122, 67, 72, 65, 70, 61, 204, 63, 66, 65, 64, 93, 130, 69, 76, 125, 166, 73, 184, 75, 86, 125, 180, 101, 190, 81, 240, 81

Offset

1,2

Comments

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

Rémy Sigrist, Scatterplot of the first 2^16 terms

Prog

(PARI) A296203(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, sigma(d)))); (v); } \\ after code in A295901.

Crossrefs

Cf. A000203, A169813, A256739, A295901, A296208.

Sequence in context: A154811 A309513 A347068 * A036237 A015948 A119733

Adjacent sequences: A296200 A296201 A296202 * A296204 A296205 A296206

Keyword

nonn

Author

Antti Karttunen, Dec 25 2017, from Rémy Sigrist's "gallery of scatter plots" in A295901.

Status

approved