A378437 -id:A378437 - cp's OEIS frontend

A378438 Dirichlet inverse of A378436, where A378436 is the inverse Möbius transform of the number of partitions of n into distinct divisors of n.

1, -2, -2, 1, -2, 3, -2, 0, 1, 4, -2, -1, -2, 4, 4, 0, -2, -1, -2, -3, 4, 4, -2, -2, 1, 4, 0, -3, -2, -8, -2, 0, 4, 4, 4, -2, -2, 4, 4, 0, -2, -7, -2, -2, -2, 4, -2, 0, 1, -2, 4, -2, -2, 0, 4, 1, 4, 4, -2, -21, -2, 4, -2, 0, 4, -7, -2, -2, 4, -8, -2, -10, -2, 4, -2, -2, 4, -6, -2, 0, 0, 4, -2, -15, 4, 4, 4, -1, -2

Offset: 1

Antti Karttunen, Nov 26 2024

sign

Equivalently, Möbius transform of the Dirichlet inverse of A033630.

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

Cf. A008683, A033630.
Dirichlet inverse of A378436.
Möbius transform of A378437.

A033630(n) = if(!n, 1, my(p=1); fordiv(n, d, p *= (1 + 'x^d)); polcoeff(p, n));
A378436(n) = sumdiv(n,d,A033630(d));
memoA378438 = Map();
A378438(n) = if(1==n,1,my(v); if(mapisdefined(memoA378438,n,&v), v, v = -sumdiv(n,d,if(dA378436(n/d)*A378438(d),0)); mapput(memoA378438,n,v); (v)));

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA378436(n/d) * a(d).

a(n) = Sum_{d|n} A008683(n/d)*A378437(d).

A378440 Dirichlet inverse of Möbius transform of A033630, where A033630 is the number of partitions of n into distinct divisors of n.

Original entry on oeis.org

1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, -3, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, -3, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, -29, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -19, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, -21, 0, 0, 0, -1, 0, -19, 0, 0, 0, 0, 0, -11, 0, 0, 0, -1

Offset: 1

Antti Karttunen, Nov 27 2024

sign

Equally, inverse Möbius transform of A378437, which is the Dirichlet inverse of A033630.

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

Inverse Möbius transform of A378437.
Dirichlet inverse of A378439.
Cf. A033630.

A033630(n) = if(!n, 1, my(p=1); fordiv(n, d, p *= (1 + 'x^d)); polcoeff(p, n));
A378439(n) = sumdiv(n, d, moebius(n/d)*A033630(d));
memoA378440 = Map();
A378440(n) = if(1==n,1,my(v); if(mapisdefined(memoA378440,n,&v), v, v = -sumdiv(n,d,if(dA378439(n/d)*A378440(d),0)); mapput(memoA378440,n,v); (v)));

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA378439(n/d) * a(d).

a(n) = Sum_{d|n} A378437(d).

cp's OEIS Frontend

A378438 Dirichlet inverse of A378436, where A378436 is the inverse Möbius transform of the number of partitions of n into distinct divisors of n.

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