A349692 Dirichlet convolution of the gcd-sum function (A018804) with itself.
1, 6, 10, 25, 18, 60, 26, 88, 67, 108, 42, 250, 50, 156, 180, 280, 66, 402, 74, 450, 260, 252, 90, 880, 211, 300, 372, 650, 114, 1080, 122, 832, 420, 396, 468, 1675, 146, 444, 500, 1584, 162, 1560, 170, 1050, 1206, 540, 186, 2800, 435, 1266, 660, 1250, 210, 2232, 756
Offset: 1
Links
- Vaclav Kotesovec, Asymptotics of Sum_{k=1..n} a(k) with a graph
Programs
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Mathematica
A018804[n_] := Sum[GCD[n,k], {k, 1, n}]; a[n_] := Sum[A018804[d] A018804[n/d], {d, Divisors[n]}]; Table[a[n], {n, 1, 55}] f[p_, e_] := (e + 1)*p^(e - 2)*((e + 2)*(e + 3)*p^2 - 2*e*(e + 2)*p + e*(e - 1))/6; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 55] (* Amiram Eldar, Nov 25 2021 *)
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PARI
A029935(n) = sumdiv(n, d, eulerphi(d)*eulerphi(n/d)); \\ From A029935. A349692(n) = sumdiv(n, d, A029935(n/d)*d*numdiv(d)); \\ Antti Karttunen, Nov 25 2021