A373923 - OEIS

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A373923

a(n) = Sum_{d|n} (-1)^pi(d).

1, 0, 2, 1, 0, 0, 2, 2, 3, 0, 0, 0, 2, 2, 2, 3, 0, 0, 2, 2, 4, 0, 0, 0, -1, 0, 2, 2, 2, 2, 0, 2, 0, -2, 0, -1, 2, 2, 4, 4, 0, 2, 2, 2, 4, 0, 0, 0, 1, -2, 0, 0, 2, 0, 0, 4, 4, 2, 0, 2, 2, 0, 6, 3, 2, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 6, 3, 0, 0, 0, -2, 0, 2, 2

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OFFSET

1,3

COMMENTS

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

LINKS

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

MAPLE

f:= proc(n) local d; add((-1)^numtheory:-pi(d), d=numtheory:-divisors(n)) end proc:

map(f, [$1..100]); # Robert Israel, Sep 13 2024

MATHEMATICA

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