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A349916
Sum of A113415 and its Dirichlet inverse, where A113415 is the arithmetic mean between the number and sum of the odd divisors of n.
5
2, 0, 0, 1, 0, 6, 0, 1, 9, 8, 0, 3, 0, 10, 24, 1, 0, 7, 0, 4, 30, 14, 0, 3, 16, 16, 21, 5, 0, 4, 0, 1, 42, 20, 40, 8, 0, 22, 48, 4, 0, 6, 0, 7, 40, 26, 0, 3, 25, 18, 60, 8, 0, 23, 56, 5, 66, 32, 0, 14, 0, 34, 53, 1, 64, 10, 0, 10, 78, 12, 0, 8, 0, 40, 70, 11, 70, 12, 0, 4, 61, 44, 0, 18, 80, 46, 96, 7, 0, 44, 80
OFFSET
1,1
LINKS
FORMULA
a(n) = A113415(n) + A349915(n).
a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1<d<n} A113415(d) * A349915(n/d).
For all n >= 1, a(4*n) = A113415(n).
MATHEMATICA
s[n_] := DivisorSum[n, (# + 1) * Mod[#, 2] &] / 2; sinv[1] = 1; sinv[n_] := sinv[n] = -DivisorSum[n, sinv[#] * s[n/#] &, # < n &]; a[n_] := s[n] + sinv[n]; Array[a, 100] (* Amiram Eldar, Dec 08 2021 *)
PROG
(PARI)
A113415(n) = if(n<1, 0, sumdiv(n, d, if(d%2, (d+1)/2)));
memoA349915 = Map();
A349915(n) = if(1==n, 1, my(v); if(mapisdefined(memoA349915, n, &v), v, v = -sumdiv(n, d, if(d<n, A113415(n/d)*A349915(d), 0)); mapput(memoA349915, n, v); (v)));
A349916(n) = (A113415(n)+A349915(n));
CROSSREFS
Cf. A113415 (also a quadrisection of this sequence), A349915.
Cf. also A349913, A349914.
Sequence in context: A335156 A158785 A346243 * A349342 A365712 A349914
KEYWORD
nonn
AUTHOR
Antti Karttunen, Dec 07 2021
STATUS
approved