A318504 SumXOR of divisors of n, up to, but not including the second largest of them A032742(n); a(1) = 0 by convention.

0, 0, 0, 1, 0, 3, 0, 3, 1, 3, 0, 4, 0, 3, 2, 7, 0, 6, 0, 2, 2, 3, 0, 10, 1, 3, 2, 0, 0, 9, 0, 15, 2, 3, 4, 7, 0, 3, 2, 0, 0, 15, 0, 12, 14, 3, 0, 22, 1, 12, 2, 10, 0, 29, 4, 6, 2, 3, 0, 26, 0, 3, 12, 31, 4, 27, 0, 22, 2, 5, 0, 5, 0, 3, 8, 20, 6, 17, 0, 4, 11, 3, 0, 14, 4, 3, 2, 18, 0, 3, 6, 16, 2, 3, 4, 46, 0, 10, 0, 5, 0, 53, 0, 24, 26

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, A106409, A178910, A227320, A318505, A318507, A318517.

Programs

PARI

A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
A318504(n) = { my(v=0); fordiv(n,d,if(d<A032742(n), v = bitxor(v,d))); (v); };

Formula

a(n) = A032742(n) XOR A227320(n).

For n > 1, a(n) = A106409(n) XOR A178910(n).