A362632 a(n) = Sum_{d|n, gcd(d,n/d)=1} d * psi(d), where psi is the Dedekind psi function (A001615).

1, 7, 13, 25, 31, 91, 57, 97, 109, 217, 133, 325, 183, 399, 403, 385, 307, 763, 381, 775, 741, 931, 553, 1261, 751, 1281, 973, 1425, 871, 2821, 993, 1537, 1729, 2149, 1767, 2725, 1407, 2667, 2379, 3007, 1723, 5187, 1893, 3325, 3379, 3871, 2257, 5005, 2745, 5257, 3991, 4575, 2863

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 + 1, p prime.

From Amiram Eldar, May 03 2023: (Start)

Multiplicative with a(p^e) = 1 + (p+1)*p^(2*e-1).

Sum_{k=1..n} a(k) ~ c * n^3, where c = (1/3) * Product_{p prime} (p^4 + p^3 + 2*p^2 + 2*p + 1)/(p^2*(p^2 + p + 1)) = 0.55359070186594463118... . (End)

Mathematica

f[p_, e_] := 1 + (p + 1)*p^(2*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: A137165 A087195 A255653 * A200270 A031887 A294943

Adjacent sequences: A362629 A362630 A362631 * A362633 A362634 A362635

Keyword

nonn,easy,mult

Author

Wesley Ivan Hurt, Apr 28 2023

Status

approved