OFFSET
1,1
COMMENTS
Question: Are all terms nonnegative?
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..16384
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
FORMULA
MATHEMATICA
k[n_] := (n/2^IntegerExponent[n, 2] + 1)/2; d[1] = 1; d[n_] := d[n] = -DivisorSum[n, d[#]*k[n/#] &, # < n &]; a[n_] := k[n] + d[n]; Array[a, 100] (* Amiram Eldar, Nov 13 2021 *)
PROG
(PARI)
up_to = 16384;
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*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.
A003602(n) = (1+(n>>valuation(n, 2)))/2;
v349134 = DirInverseCorrect(vector(up_to, n, A003602(n)));
A349134(n) = v349134[n];
(PARI) A349135(n) = if(1==n, 2, -sumdiv(n, d, if(1==d||n==d, 0, A003602(d)*A349134(n/d)))); \\ (Demonstrates the "cut convolution" formula) - Antti Karttunen, Nov 13 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 13 2021
STATUS
approved