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

Author

Antti Karttunen, Dec 25 2017

Keywords

• nonn
• base

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

Crossrefs

Cf. A003987, A256739, A295901, A296207.

Programs

PARI

A256739(n) = { if(1==n,return(n)); my(x=n); fordiv(n,d,if(dA256739(d)))); (x); };
A296206(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, A256739(d)))); (v); } \\ after code in A295901.