A092349 a(n) = sigma_3(n) - sigma_2(n).

0, 4, 18, 52, 100, 202, 294, 500, 666, 1004, 1210, 1834, 2028, 2846, 3268, 4340, 4624, 6358, 6498, 8652, 9132, 11378, 11638, 15530, 15100, 18932, 19620, 24062, 23548, 30452, 28830, 36084, 36076, 42776, 42044, 53350, 49284, 59930, 59844, 71500, 67240, 84188

Offset

1,2

Links

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

Formula

G.f.: Sum_{k>=1} k^2*(k - 1)*x^k/(1 - x^k). - Ilya Gutkovskiy, Mar 17 2017

From Amiram Eldar, Jan 01 2025: (Start)

Dirichlet g.f.: zeta(s) * (zeta(s-3) - zeta(s-2)).

Sum_{k=1..n} a(k) ~ (zeta(4)/4) * n^4. (End)

Mathematica

a[n_] := Subtract @@ DivisorSigma[{3, 2}, n]; Array[a, 50] (* Amiram Eldar, Jan 01 2025 *)

Prog

(PARI) a(n) = my(f = factor(n)); sigma(f, 3) - sigma(f, 2); \\ Amiram Eldar, Jan 01 2025

Crossrefs

Cf. A001157, A001158, A013662.

Sequence in context: A256431 A256430 A225263 * A027659 A059133 A300493

Adjacent sequences: A092346 A092347 A092348 * A092350 A092351 A092352

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 20 2004

Status

approved