

A296207


XorMoebius transform of A227320, binary XOR of proper divisors of n.


5



0, 1, 1, 2, 1, 0, 1, 4, 3, 6, 1, 0, 1, 4, 7, 8, 1, 12, 1, 12, 5, 8, 1, 0, 5, 14, 9, 8, 1, 6, 1, 16, 9, 18, 3, 24, 1, 16, 15, 24, 1, 26, 1, 16, 5, 20, 1, 0, 7, 22, 19, 28, 1, 0, 15, 16, 17, 30, 1, 12, 1, 28, 31, 32, 9, 58, 1, 36, 21, 38, 1, 48, 1, 38, 19, 32, 13, 54, 1, 48, 27, 42, 1, 52, 21, 40, 31, 32, 1, 34, 11, 40, 29, 44, 23, 0, 1
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OFFSET

1,4


COMMENTS

Unique sequence satisfying SumXOR_{d divides n} a(d) = A227320(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 XorMoebius transform.


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384
Index entries for sequences related to binary expansion of n


FORMULA

a(n) = n XOR A256739(n), where XOR is the bitwise XORoperation (A003987).


PROG

(PARI)
A227320(n) = { my(s=0); fordiv(n, d, if(d<n, s = bitxor(s, d))); s; };
A296207(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, A227320(d)))); (v); } \\ after code in A295901.


CROSSREFS

Cf. A003987, A178910, A227320, A256739, A295901, A296206.
Cf. A297107 (positions of zeros).
Sequence in context: A004248 A034373 A238889 * A253628 A102728 A262495
Adjacent sequences: A296204 A296205 A296206 * A296208 A296209 A296210


KEYWORD

nonn,base


AUTHOR

Antti Karttunen, Dec 25 2017


STATUS

approved



