A323408 -id:A323408 - cp's OEIS frontend

A323403 Sum of sigma and its Dirichlet inverse: a(n) = A000203(n) + A046692(n).

2, 0, 0, 9, 0, 24, 0, 15, 16, 36, 0, 20, 0, 48, 48, 31, 0, 30, 0, 30, 64, 72, 0, 60, 36, 84, 40, 40, 0, 0, 0, 63, 96, 108, 96, 97, 0, 120, 112, 90, 0, 0, 0, 60, 60, 144, 0, 124, 64, 78, 144, 70, 0, 120, 144, 120, 160, 180, 0, 216, 0, 192, 80, 127, 168, 0, 0, 90, 192, 0, 0, 195, 0, 228, 104, 100, 192, 0, 0, 186, 121, 252, 0, 288, 216, 264, 240, 180, 0, 288

Offset: 1

Antti Karttunen, Jan 15 2019

nonn

Antti Karttunen, Table of n, a(n) for n = 1..16384
Index entries for sequences related to sigma(n)

Cf. A000203, A046692.

Cf. also A319340, A322581, A323364, A323399, A323408.

up_to = 16384;
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); };
v046692 = DirInverse(vector(up_to,n,sigma(n)));
A046692(n) = v046692[n];
A323403(n) = (sigma(n)+A046692(n));

a(n) = A000203(n) + A046692(n).

A323407 Dirichlet inverse of A047994, unitary phi.

Original entry on oeis.org

1, -1, -2, -2, -4, 2, -6, -2, -4, 4, -10, 4, -12, 6, 8, 0, -16, 4, -18, 8, 12, 10, -22, 4, -8, 12, -2, 12, -28, -8, -30, 4, 20, 16, 24, 8, -36, 18, 24, 8, -40, -12, -42, 20, 16, 22, -46, 0, -12, 8, 32, 24, -52, 2, 40, 12, 36, 28, -58, -16, -60, 30, 24, 8, 48, -20, -66, 32, 44, -24, -70, 8, -72, 36, 16, 36, 60, -24, -78, 0, 8, 40, -82, -24

Offset: 1

Antti Karttunen, Jan 15 2019

sign

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

Cf. A047994, A323408.

Cf. also A023900.

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];

cp's OEIS Frontend

A323403 Sum of sigma and its Dirichlet inverse: a(n) = A000203(n) + A046692(n).

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