A296207 - OEIS

A296207

Xor-Moebius transform of A227320, binary XOR of proper divisors of n.

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 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

FORMULA

a(n) = n XOR A256739(n), where XOR is the bitwise XOR-operation (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).