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

1,1

Links

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

Index entries for sequences related to sigma(n)

Formula

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

Prog

(PARI)
up_to = 16384;
DirInverse(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = -sumdiv(n, d, if(d<n, v[n/d]*u[d], 0))); (u) }; \\ Compute the Dirichlet inverse of the sequence given in input vector v.
A047994(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));

Crossrefs

Cf. A000203, A046692.

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

Sequence in context: A323896 A345065 A323364 * A346238 A347085 A347091

Adjacent sequences: A323400 A323401 A323402 * A323404 A323405 A323406

Keyword

nonn

Author

Antti Karttunen, Jan 15 2019

Status

approved