0,3

Also the convolution of A080054 and A048272.

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Mircea Merca, Combinatorial interpretations of a recent convolution for the number of divisors of a positive integer, Journal of Number Theory, Volume 160, March 2016, Pages 60-75, corollary 3.4

a(n) = Sum_{k=0..n} A015723(k)*A000700(n-k).

a(n) ~ log(2) * exp(Pi*sqrt(n/2)) / (Pi * 2^(3/4) * n^(1/4)). - Vaclav Kotesovec, Sep 14 2021

with(numtheory):

b:= proc(n) option remember; `if`(n=0, 1, add(add(d*

[0, 2, -1, 2][1+irem(d, 4)], d=divisors(j))*b(n-j), j=1..n)/n)

end:

g:= proc(n) option remember; add((-1)^(d+1), d=divisors(n)) end:

a:= n-> add(b(j)*g(n-j), j=0..n):

seq(a(n), n=0..60); # Alois P. Heinz, Jun 18 2016

q[n_, k_] := q[n, k] = If[n < k || k < 1, 0, If[n == 1, 1, q[n - k, k] + q[n - k, k - 1]]]; Table[Sum[SeriesCoefficient[Product[1 + x^j, {j, 1, k, 2}], {x, 0, k}] Sum[i q[#, i], {i, 1, Floor[(Sqrt[8 # + 1] - 1)/2]}] &[n - k], {k, 0, n}], {n, 0, 45}] (* Michael De Vlieger, Jun 18 2016, after Vaclav Kotesovec at A015723 and Vladimir Reshetnikov at A000700 *)

Cf. A015723, A000700, A080054, A048272.

Sequence in context: A032705 A332639 A281168 * A343328 A088762 A217385

Adjacent sequences: A274349 A274350 A274351 * A274353 A274354 A274355

R. J. Mathar, Jun 18 2016

approved