A318457 a(n) = n XOR A001065(n), where XOR is bitwise-xor (A003987) and A001065 = sum of proper divisors.

1, 3, 2, 7, 4, 0, 6, 15, 13, 2, 10, 28, 12, 4, 6, 31, 16, 7, 18, 2, 30, 24, 22, 60, 31, 10, 22, 0, 28, 52, 30, 63, 46, 54, 46, 19, 36, 48, 54, 26, 40, 28, 42, 4, 12, 52, 46, 124, 57, 25, 38, 26, 52, 116, 38, 120, 46, 26, 58, 80, 60, 28, 22, 127, 82, 12, 66, 126, 94, 12, 70, 51, 72, 98, 122, 12, 94, 20, 78, 58, 121, 126, 82, 216, 66

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, A001065, A003987, A033879, A318456, A318458, A318467.

Cf. A000396 (positions of zeros).

Programs

Mathematica

Array[BitXor[#, DivisorSigma[1, #] - #] &, 100] (* Paolo Xausa, Dec 16 2024 *)

PARI

A318457(n) = bitxor(n,sigma(n)-n);

Formula

a(n) = A003987(n, A001065(n)).

a(n) = A000203(n) - 2*A318458(n).