A378532 -id:A378532 - cp's OEIS frontend

A378531 Dirichlet convolution of A378432 and A378542.

1, 0, 0, 2, 0, 3, 0, 2, 2, 3, 0, 4, 0, 3, 3, 6, 0, 4, 0, 4, 3, 3, 0, 14, 2, 3, 2, 4, 0, 6, 0, 10, 3, 3, 3, 18, 0, 3, 3, 14, 0, 6, 0, 4, 4, 3, 0, 30, 2, 4, 3, 4, 0, 14, 3, 14, 3, 3, 0, 30, 0, 3, 4, 22, 3, 6, 0, 4, 3, 6, 0, 48, 0, 3, 4, 4, 3, 6, 0, 30, 6, 3, 0, 30, 3, 3, 3, 14, 0, 30, 3, 4, 3, 3, 3, 74, 0, 4, 4, 18

Offset: 1

Antti Karttunen, Dec 01 2024

nonn

Möbius transform of A378533.

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A008683, A378532 (Dirichlet inverse), A378432, A378533 (inverse Möbius transform), A378542.

Cf. also A345182.

A033879(n) = ((2*n)-sigma(n));
A296075(n) = sumdiv(n,d,A033879(d));
memoA378432 = Map();
A378432(n) = if(1==n,1,my(v); if(mapisdefined(memoA378432,n,&v), v, v = -sumdiv(n,d,if(dA296075(n/d)*A378432(d),0)); mapput(memoA378432,n,v); (v)));
A378542(n) = sumdiv(n,d,d*!(bigomega(n/d)%2));
A378531(n) = sumdiv(n,d,A378432(d)*A378542(n/d));

a(n) = Sum_{d|n} A378432(d)*A378542(n/d).

a(n) = Sum_{d|n} A008683(d)*A378533(n/d).

A378534 Dirichlet convolution of A033879 and A378525.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Dec 01 2024

sign

Möbius transform of A378532.

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

Cf. A008683, A033879, A323910, A378532 (inverse Möbius transform), A378533 (Dirichlet inverse), A378542.

Cf. also A378224.

A033879(n) = (n+n-sigma(n));
A378542(n) = sumdiv(n,d,d*!(bigomega(n/d)%2));
memoA378525 = Map();
A378525(n) = if(1==n,1,my(v); if(mapisdefined(memoA378525,n,&v), v, v = -sumdiv(n,d,if(dA378542(n/d)*A378525(d),0)); mapput(memoA378525,n,v); (v)));
A378534(n) = sumdiv(n,d,A033879(d)*A378525(n/d));

a(n) = Sum_{d|n} A033879(d)*A378525(n/d).

a(n) = Sum_{d|n} A008683(d)*A378532(n/d).

cp's OEIS Frontend

A378531 Dirichlet convolution of A378432 and A378542.

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