A318517 a(n) = A032742(n) XOR n-A032742(n), where XOR is bitwise-xor (A003987) and A032742 = the largest proper divisor of n.

1, 0, 3, 0, 5, 0, 7, 0, 5, 0, 11, 0, 13, 0, 15, 0, 17, 0, 19, 0, 9, 0, 23, 0, 17, 0, 27, 0, 29, 0, 31, 0, 29, 0, 27, 0, 37, 0, 23, 0, 41, 0, 43, 0, 17, 0, 47, 0, 45, 0, 51, 0, 53, 0, 39, 0, 53, 0, 59, 0, 61, 0, 63, 0, 57, 0, 67, 0, 57, 0, 71, 0, 73, 0, 43, 0, 73, 0, 79, 0, 45, 0, 83, 0, 85, 0, 39, 0, 89, 0, 67, 0, 33, 0, 95

Offset: 1

Author

Antti Karttunen, Aug 28 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

Crossrefs

Cf. A003987, A032742, A060681, A106409, A318507, A318516, A318518.

Programs

PARI

A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
A318517(n) = bitxor(A032742(n),n-A032742(n));

Formula

a(n) = A003987(A032742(n), A060681(n)).

a(n) = n - 2*A318518(n).