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

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Dedekind Function.

Wikipedia, Dedekind psi function.

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)

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 *)

Crossrefs

Cf. A001615 (psi), A034444, A060648.

Sequence in context: A087202 A270037 A319132 * A322757 A010666 A196001

Adjacent sequences: A362621 A362622 A362623 * A362625 A362626 A362627

Keyword

nonn,easy,mult

Author

Wesley Ivan Hurt, Apr 28 2023

Status

approved