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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 (list; graph; refs; listen; history; text; internal format)
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

Antti Karttunen, Table of n, a(n) for n = 1..65537

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.

CROSSREFS

Cf. A001065, A051953, A256739, A295901, A296203, A318501, A318502.

Sequence in context: A243146 A048671 A205959 * A088123 A050932 A286515

Adjacent sequences:  A318500 A318501 A318502 * A318504 A318505 A318506

KEYWORD

nonn

AUTHOR

Antti Karttunen, Aug 28 2018

STATUS

approved

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Last modified October 16 15:51 EDT 2019. Contains 328101 sequences. (Running on oeis4.)