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A323910 Dirichlet inverse of deficiency of n, A033879. 9
1, -1, -2, 0, -4, 4, -6, 0, -1, 6, -10, 2, -12, 8, 10, 0, -16, 1, -18, 2, 14, 12, -22, 4, -3, 14, -2, 2, -28, -16, -30, 0, 22, 18, 26, 4, -36, 20, 26, 4, -40, -24, -42, 2, 4, 24, -46, 8, -5, -1, 34, 2, -52, 0, 42, 4, 38, 30, -58, 2, -60, 32, 6, 0, 50, -40, -66, 2, 46, -40, -70, 12, -72, 38, 2, 2, 62, -48, -78, 8, -4, 42, -82, -2, 66, 44, 58, 4, -88, 2, 74, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
MATHEMATICA
b[n_] := 2 n - DivisorSigma[1, n];
a[n_] := a[n] = If[n == 1, 1, -Sum[b[n/d] a[d], {d, Most@ Divisors[n]}]];
Array[a, 100] (* Jean-François Alcover, Feb 17 2020 *)
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];
CROSSREFS
Sequence in context: A363062 A316987 A228885 * A166085 A129760 A291330
KEYWORD
sign
AUTHOR
Antti Karttunen, Feb 12 2019
STATUS
approved

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Last modified March 29 08:08 EDT 2024. Contains 371265 sequences. (Running on oeis4.)