A327987 a(n) = Sum_{d|n} d & (n/d), where & is the bitwise AND operator, with a(0) = 0.

0, 1, 0, 2, 2, 2, 4, 2, 0, 5, 0, 2, 4, 2, 4, 4, 4, 2, 4, 2, 12, 8, 4, 2, 8, 7, 0, 4, 12, 2, 16, 2, 0, 8, 0, 12, 10, 2, 4, 4, 0, 2, 16, 2, 4, 10, 4, 2, 8, 9, 0, 4, 12, 2, 8, 4, 8, 8, 0, 2, 24, 2, 4, 6, 8, 12, 8, 2, 4, 8, 16, 2, 24, 2, 0, 14, 4, 8, 16, 2, 24, 17

Offset: 0

Author

Peter Luschny, Oct 11 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16384

Crossrefs

Cf. A327988 (zeros), A327989, A016754.

Programs

Julia

using IntegerSequences
vcat([0], [V327987(n) for n in 1:81]) |> println  # Peter Luschny, Sep 25 2021

Magma

[0] cat [&+[BitwiseAnd(d,n div d):d in Divisors(n)]:n in [1..90]]; // Marius A. Burtea, Oct 11 2019

Maple

A327987 := n -> add(Bits:-And(d, n/d), d=numtheory:-divisors(n)):
seq(A327987(n), n=0..81);

Mathematica

divisors[0] := {}; divisors[n_] := Divisors[n];
a[n_] := Total[Table[BitAnd[d , n/d], {d, divisors[n]}]] ;
Table[a[n], {n, 0, 81}]

PARI

a(n) = if (n, sumdiv(n, d, bitand(d, n/d)), 0); \\ Michel Marcus, Oct 11 2019

Sage

def a(n): return sum(d & n//d for d in divisors(n)) if n > 0 else 0
print([a(n) for n in (0..81)])

Formula

a(n) is odd if and only if n is an odd square (A016754).