A373924 a(n) = Sum_{d|n} (-1)^pi(d) * mu(n/d).

1, -2, 0, 2, -2, 0, 0, 0, 0, 4, -2, -2, 0, 2, 2, 0, -2, 0, 0, -2, 0, 4, -2, 0, 0, 0, -2, -4, 0, -2, -2, -2, 0, 2, 0, 0, 0, 2, 0, 0, -2, -2, 0, -2, 0, 4, -2, 0, -2, -2, 0, -2, 0, 4, 4, 2, 0, 2, -2, 0, 0, 4, 0, 2, 2, 0, -2, -2, 0, -4, 0, 2, -2, 0, -2, -4, 0, 0, 0, 0, 2

Offset: 1

Author

Wesley Ivan Hurt, Jun 22 2024

Keywords

• sign

Comments

Möbius transform of (-1)^pi(n) (A065357).

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000720 (pi), A008683 (mu), A065357, A373923.

Programs

Maple

f:= proc(n) local d; add((-1)^numtheory:-pi(d)*numtheory:-mobius(n/d),d=numtheory:-divisors(n)) end proc:
map(f, [$1..100]); # Robert Israel, Sep 13 2024

Mathematica

Table[DivisorSum[n, (-1)^PrimePi[#] MoebiusMu[n/#] &], {n, 100}]