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

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

1,2

Links

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

Formula

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

Example

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)

Maple

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A198017 A137351 A134406 * A242719 A242489 A074789

Adjacent sequences: A099975 A099976 A099977 * A099979 A099980 A099981

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 19 2004

Extensions

More terms from Emeric Deutsch, Dec 07 2004

Edited by M. F. Hasler, Mar 06 2017

Status

approved