A296208 Xor-Moebius transform of A005187.

1, 2, 5, 4, 9, 12, 10, 8, 20, 24, 18, 24, 22, 16, 23, 16, 33, 60, 34, 48, 41, 56, 43, 48, 39, 36, 34, 40, 55, 52, 56, 32, 86, 96, 65, 120, 70, 104, 88, 96, 78, 104, 83, 120, 88, 112, 88, 96, 84, 84, 71, 80, 103, 104, 115, 80, 72, 68, 112, 96, 116, 76, 75, 64, 158, 244, 130, 192, 168, 192, 139, 240, 142, 212, 175, 216

Offset: 1

Author

Antti Karttunen, Dec 25 2017

Keywords

• nonn
• base

Comments

Unique sequence satisfying SumXOR_{d divides n} a(d) = A005187(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. A297111 gives the ordinary Möbius transform of A005187.

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, A005187, A256739, A294899, A295901, A296203, A297110, A297111.

Programs

PARI

A005187(n) = { my(s=n); while(n>>=1, s+=n); s; };
A296208(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, A005187(d)))); (v); } \\ after code in A295901.