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

1,1

Links

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

Formula

a(n) = A033879(n) + A323910(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.
A033879(n) = (2*n-sigma(n));
v323910 = DirInverse(vector(up_to, n, A033879(n)));
A323910(n) = v323910[n];
A323911(n) = (A033879(n)+A323910(n));

Crossrefs

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

Sequence in context: A353336 A349126 A340188 * A322581 A347083 A209915

Adjacent sequences: A323908 A323909 A323910 * A323912 A323913 A323914

Keyword

sign

Author

Antti Karttunen, Feb 12 2019

Status

approved