A378453 -id:A378453 - cp's OEIS frontend

A378452 Dirichlet inverse of A007875, where A007875(n) = phi(2^omega(n)).

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

Offset: 1

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Antti Karttunen, Nov 29 2024

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Inverse Möbius transform of A378453.

Antti Karttunen, Table of n, a(n) for n = 1..20000

Cf. A007875, A378453 (Möbius transform).

A007875(n) = eulerphi(2^omega(n));
memoA378452 = Map();
A378452(n) = if(1==n,1,my(v); if(mapisdefined(memoA378452,n,&v), v, v = -sumdiv(n,d,if(dA007875(n/d)*A378452(d),0)); mapput(memoA378452,n,v); (v)));

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA007875(n/d) * a(d).

a(n) = Sum_{d|n} A378453(d).

cp's OEIS Frontend

A378452 Dirichlet inverse of A007875, where A007875(n) = phi(2^omega(n)).

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