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A296208
Xor-Moebius transform of A005187.
4
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
1,2
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.
PROG
(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.
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Dec 25 2017
STATUS
approved