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A318503
Xor-Moebius transform of A001065, the sum of proper divisors.
3
0, 1, 1, 2, 1, 6, 1, 4, 5, 8, 1, 20, 1, 10, 9, 8, 1, 22, 1, 28, 11, 14, 1, 48, 7, 16, 9, 20, 1, 44, 1, 16, 15, 20, 13, 52, 1, 22, 17, 32, 1, 48, 1, 36, 45, 26, 1, 96, 9, 36, 21, 60, 1, 94, 17, 88, 23, 32, 1, 76, 1, 34, 39, 32, 19, 72, 1, 44, 27, 68, 1, 120, 1, 40, 63, 84, 19, 92, 1, 80, 37, 44, 1, 184, 23, 46, 33, 112, 1, 132
OFFSET
1,4
COMMENTS
Unique sequence satisfying SumXOR_{d divides n} a(d) = sigma(n)-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
FORMULA
a(n) = A318501(n) XOR A318502(n).
PROG
(PARI) A318503(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, sigma(d)-d))); (v); } \\ after code in A295901.
KEYWORD
nonn
AUTHOR
Antti Karttunen, Aug 28 2018
STATUS
approved