A318463 a(n) = Sum_{d|n, d < n/d} (d AND n/d), where AND is bitwise-and (A004198).

0, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 2, 2, 0, 1, 2, 1, 6, 4, 2, 1, 4, 1, 0, 2, 6, 1, 8, 1, 0, 4, 0, 6, 2, 1, 2, 2, 0, 1, 8, 1, 2, 5, 2, 1, 4, 1, 0, 2, 6, 1, 4, 2, 4, 4, 0, 1, 12, 1, 2, 3, 0, 6, 4, 1, 2, 4, 8, 1, 12, 1, 0, 7, 2, 4, 8, 1, 12, 4, 0, 1, 16, 2, 2, 2, 12, 1, 16, 6, 6, 4, 2, 2, 8, 1, 6, 11, 6, 1, 4, 1, 8, 16

Offset: 1

Author

Antti Karttunen, Aug 28 2018

Keywords

• nonn
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences related to binary expansion of n
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A004198, A318458, A318460, A318461, A318462.

Programs

PARI

A318463(n) = { my(ands=0); fordiv(n,d,if(d<(n/d), ands += bitand(d,n/d))); (ands); };

Formula

a(n) = A000203(n) - A318461(n) = (A000203(n)-A318462(n))/2.