A318467 a(n) = 2*n XOR A000203(n), where XOR is bitwise-xor (A003987) and A000203 = sum of divisors.

3, 7, 2, 15, 12, 0, 6, 31, 31, 6, 26, 4, 20, 4, 6, 63, 48, 3, 50, 2, 10, 8, 54, 12, 45, 30, 30, 0, 36, 116, 30, 127, 114, 114, 118, 19, 108, 112, 118, 10, 120, 52, 122, 12, 20, 20, 110, 28, 91, 57, 46, 10, 92, 20, 38, 8, 34, 46, 74, 208, 68, 28, 22, 255, 214, 20, 194, 246, 234, 28, 198, 83, 216, 230, 234, 20, 250, 52, 206, 26

Offset: 1

Author

Antti Karttunen, Aug 26 2018

Keywords

• nonn
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences related to binary expansion of n
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A003987, A318457, A318458, A318466, A318468.

Cf. A000396 (positions of zeros), A378227 (XOR-Moebius transform), A379234 (fixed points), A379236.

Cf. also A294899, A318457, A378988.

Programs

Mathematica

Table[BitXor[2n,DivisorSigma[1,n]],{n,80}] (* Harvey P. Dale, Oct 30 2022 *)

PARI

A318467(n) = bitxor(2*n,sigma(n));

Formula

a(n) = A003987(2*n, A000203(n)).

a(n) = A224880(n) - 2*A318468(n).

a(n) = 2*n XOR (A318457(n)+2*A318458(n)). - Antti Karttunen, Jan 08 2025