A099979 -id:A099979 - cp's OEIS frontend

A283237 a(n) = sigma_2(3*n).

10, 50, 91, 210, 260, 455, 500, 850, 820, 1300, 1220, 1911, 1700, 2500, 2366, 3410, 2900, 4100, 3620, 5460, 4550, 6100, 5300, 7735, 6510, 8500, 7381, 10500, 8420, 11830, 9620, 13650, 11102, 14500, 13000, 17220, 13700, 18100, 15470, 22100, 16820, 22750, 18500

Offset: 1

Seiichi Manyama, Mar 03 2017

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Sigma_2(k*n): A001157 (k=1), A099979 (k=2), this sequence (k=3).

Cf. A002117.

Table[DivisorSigma[2,3n],{n,1,43}] (* Indranil Ghosh, Mar 03 2017 *)

a(n) = sigma(3*n,2); \\ Indranil Ghosh, Mar 03 2017

a(n) = A001157(3*n).

Sum_{k=1..n} a(k) ~ (29*zeta(3)/9) * n^3. - Amiram Eldar, Dec 12 2023

A099978 Bisection of A001157: a(n) = sigma_2(2n-1).

Original entry on oeis.org

1, 10, 26, 50, 91, 122, 170, 260, 290, 362, 500, 530, 651, 820, 842, 962, 1220, 1300, 1370, 1700, 1682, 1850, 2366, 2210, 2451, 2900, 2810, 3172, 3620, 3482, 3722, 4550, 4420, 4490, 5300, 5042, 5330, 6510, 6100, 6242, 7381, 6890, 7540, 8420, 7922, 8500

Offset: 1

N. J. A. Sloane, Nov 19 2004

			From _M. F. Hasler_, Mar 06 2017: (Start)
a(1) = sigma_2(2*1-1) = 1.
a(2) = sigma_2(2*2-1) = 1 + 3^2 = 10.
a(5) = sigma_2(2*5-1) = 1 + 3^2 + 9^2 = 91. (End)
G.f.: A(x) = x + 10*x^2 + 26*x^3 + 50*x^4 + 91*x^5 + 122*x^6 + 170*x^7 + 260*x^8 + 290*x^9 + 362*x^10 + 500*x^11 + 530*x^12 + ... where A(x) = x/(1 - x) + 3^2*x^2/(1 - x^3) + 5^2*x^3/(1 - x^5) + 7^2*x^4/(1 - x^7) + 9^2*x^5/(1 - x^9) + .... - _Paul D. Hanna_, Jun 23 2025

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

Cf. A099979(n) = sigma_2(2n), the other bisection of A001157.

Cf. A283224.

with(numtheory): A099978 := n->sigma[2](2*n-1): seq(A099978(n), n=1..60);

DivisorSigma[2, Range[1, 91, 2]] (* Amiram Eldar, Aug 17 2019 *)

A099978(n)=sigma(2*n-1,2) \\ M. F. Hasler, Mar 06 2017

a(n) = A001157(2n-1) = sigma_2(2n-1). - M. F. Hasler, Mar 06 2017
Sum_{k=1..n} a(k) ~ 7*zeta(3)*n^3/6. - Vaclav Kotesovec, Aug 07 2022
G.f.: Sum_{n>=1} (2*n-1)^2 * x^n / (1 - x^(2*n-1)). - Paul D. Hanna, Jun 23 2025

More terms from Emeric Deutsch, Dec 07 2004

Edited by M. F. Hasler, Mar 06 2017

cp's OEIS Frontend

A283237 a(n) = sigma_2(3*n).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula