A296206 Xor-Moebius transform applied twice to natural numbers.

1, 2, 3, 5, 5, 6, 7, 10, 8, 10, 11, 15, 13, 14, 15, 20, 17, 16, 19, 17, 21, 22, 23, 30, 24, 26, 24, 27, 29, 30, 31, 40, 33, 34, 35, 40, 37, 38, 39, 34, 41, 42, 43, 39, 40, 46, 47, 60, 48, 48, 51, 57, 53, 48, 55, 54, 57, 58, 59, 51, 61, 62, 56, 80, 65, 66, 67, 85, 69, 70, 71, 80, 73, 74, 72, 95, 77, 78, 79, 68, 88

Offset

1,2

Comments

Xor-Moebius transform of A256739, in other words, the unique sequence that satisfies SumXOR_{d divides n} a(d) = A256739(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

Index entries for sequences related to binary expansion of n

Prog

(PARI)
A256739(n) = { if(1==n, return(n)); my(x=n); fordiv(n, d, if(d<n, x = bitxor(x, A256739(d)))); (x); };
A296206(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, A256739(d)))); (v); } \\ after code in A295901.

Crossrefs

Cf. A003987, A256739, A295901, A296207.

Sequence in context: A029910 A063677 A078903 * A079228 A373188 A067535

Adjacent sequences: A296203 A296204 A296205 * A296207 A296208 A296209

Keyword

nonn,base

Author

Antti Karttunen, Dec 25 2017

Status

approved