

A297110


XorMoebius transform of A006068, inverse of the binary Gray code.


4



1, 2, 3, 4, 7, 4, 4, 8, 12, 8, 12, 8, 8, 12, 15, 16, 31, 20, 28, 16, 31, 20, 27, 16, 23, 24, 28, 24, 23, 16, 20, 32, 48, 32, 63, 40, 56, 36, 48, 32, 48, 32, 51, 40, 48, 44, 52, 32, 36, 56, 63, 48, 39, 36, 47, 48, 48, 56, 44, 32, 40, 60, 63, 64, 112, 80, 124, 64, 96, 64, 123, 80, 112, 72, 111, 72, 127, 80, 116, 64
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OFFSET

1,2


COMMENTS

Unique sequence satisfying SumXOR_{d divides n} a(d) = A006068(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 the XorMoebius 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)
A006068(n)= { my(s=1, ns); while(1, ns = n >> s; if(0==ns, break()); n = bitxor(n, ns); s <<= 1; ); return (n); } \\ Essentially Joerg Arndt's Jul 19 2012 code.
A297110(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, A006068(d)))); (v); };


CROSSREFS

Cf. A006068, A256739, A295901, A296208.
Sequence in context: A072717 A139072 A021430 * A267695 A138676 A297111
Adjacent sequences: A297107 A297108 A297109 * A297111 A297112 A297113


KEYWORD

nonn,base


AUTHOR

Antti Karttunen, Dec 25 2017


STATUS

approved



