A323403 -id:A323403 - cp's OEIS frontend

A323911 Sum of deficiency of n (A033879) and its Dirichlet inverse.

2, 0, 0, 1, 0, 4, 0, 1, 4, 8, 0, -2, 0, 12, 16, 1, 0, -2, 0, 0, 24, 20, 0, -8, 16, 24, 12, 2, 0, -28, 0, 1, 40, 32, 48, -15, 0, 36, 48, -6, 0, -36, 0, 6, 16, 44, 0, -20, 36, 6, 64, 8, 0, -12, 80, -4, 72, 56, 0, -46, 0, 60, 28, 1, 96, -52, 0, 12, 88, -44, 0, -39, 0, 72, 28, 14, 120, -60, 0, -18, 37, 80, 0, -58, 128, 84, 112, 0, 0, -52, 144, 18

Offset: 1

Antti Karttunen, Feb 12 2019

sign

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

Cf. A033879, A297159, A323403, A323910, A323913.

up_to = 16384;
DirInverse(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = -sumdiv(n, d, if(dA033879(n) = (2*n-sigma(n));
v323910 = DirInverse(vector(up_to,n,A033879(n)));
A323910(n) = v323910[n];
A323911(n) = (A033879(n)+A323910(n));

a(n) = A033879(n) + A323910(n).

A323408 Sum of unitary phi and its Dirichlet inverse: a(n) = A047994(n) + A323407(n).

Original entry on oeis.org

2, 0, 0, 1, 0, 4, 0, 5, 4, 8, 0, 10, 0, 12, 16, 15, 0, 12, 0, 20, 24, 20, 0, 18, 16, 24, 24, 30, 0, 0, 0, 35, 40, 32, 48, 32, 0, 36, 48, 36, 0, 0, 0, 50, 48, 44, 0, 30, 36, 32, 64, 60, 0, 28, 80, 54, 72, 56, 0, 8, 0, 60, 72, 71, 96, 0, 0, 80, 88, 0, 0, 64, 0, 72, 64, 90, 120, 0, 0, 60, 88, 80, 0, 12, 128, 84, 112, 90, 0, 16, 144, 110, 120

Offset: 1

Antti Karttunen, Jan 15 2019

nonn

Antti Karttunen, Table of n, a(n) for n = 1..16384

Cf. A047994, A323407.

Cf. also A319340, A322581, A323364, A323399, A323403.

up_to = 65537;
DirInverse(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = -sumdiv(n, d, if(dA047994(n) = { my(f=factor(n)~); prod(i=1, #f, (f[1, i]^f[2, i])-1); };
v323407 = DirInverse(vector(up_to,n,A047994(n)));
A323407(n) = v323407[n];
A323408(n) = (A047994(n) + A323407(n));

cp's OEIS Frontend

A323911 Sum of deficiency of n (A033879) and its Dirichlet inverse.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula