A362624 a(n) = Sum_{d|n, gcd(d,n/d)=1} psi(d), where psi is the Dedekind psi function (A001615).

1, 4, 5, 7, 7, 20, 9, 13, 13, 28, 13, 35, 15, 36, 35, 25, 19, 52, 21, 49, 45, 52, 25, 65, 31, 60, 37, 63, 31, 140, 33, 49, 65, 76, 63, 91, 39, 84, 75, 91, 43, 180, 45, 91, 91, 100, 49, 125, 57, 124, 95, 105, 55, 148, 91, 117, 105, 124, 61, 245, 63, 132, 117, 97, 105, 260, 69, 133

Offset: 1

Author

Wesley Ivan Hurt, Apr 28 2023

Keywords

• nonn
• easy
• mult

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Dedekind Function.
• Wikipedia, Dedekind psi function.

Crossrefs

Cf. A001615 (psi), A034444, A060648.

Programs

Mathematica

f[p_, e_] := 1 + (p + 1)*p^(e - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, May 03 2023 *)

Formula

a(p) = p + 2, p prime.

From Amiram Eldar, May 03 2023: (Start)

Multiplicative with a(p^e) = 1 + (p+1)*p^(e-1).

Sum_{k=1..n} a(k) ~ c * n^2, where c = (1/2) * Product_{p prime} (1/p^2 + 1/p + p/(1 + p)) = 1.00068765086778318519... . (End)