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A349345
Sum of A109168 and its Dirichlet inverse, where A109168(n) = (n+A006519(n))/2, and A006519 is the highest power of 2 dividing n.
2
2, 0, 0, 4, 0, 8, 0, 8, 4, 12, 0, 8, 0, 16, 12, 16, 0, 12, 0, 12, 16, 24, 0, 16, 9, 28, 12, 16, 0, 8, 0, 32, 24, 36, 24, 20, 0, 40, 28, 24, 0, 12, 0, 24, 26, 48, 0, 32, 16, 34, 36, 28, 0, 32, 36, 32, 40, 60, 0, 32, 0, 64, 36, 64, 42, 20, 0, 36, 48, 24, 0, 40, 0, 76, 46, 40, 48, 24, 0, 48, 37, 84, 0, 44, 54, 88, 60, 48
OFFSET
1,1
LINKS
FORMULA
a(n) = A109168(n) + A349344(n).
a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1<d<n} A109168(d) * A349344(n/d).
For all n >= 1, a(4*n) = 4*A109168(n). - Antti Karttunen, Dec 07 2021
PROG
(PARI)
up_to = 20000;
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.
A109168(n) = ((n+bitand(n, -n))\2); \\ From A109168
v349344 = DirInverseCorrect(vector(up_to, n, A109168(n)));
A349344(n) = v349344[n];
A349345(n) = (A109168(n)+A349344(n));
CROSSREFS
Sequence in context: A323900 A349347 A354187 * A349357 A071390 A354350
KEYWORD
nonn,look
AUTHOR
Antti Karttunen, Nov 15 2021
STATUS
approved