A160664 a(n) = a(n-1) + A000203(n), a(0)=1.

1, 2, 5, 9, 16, 22, 34, 42, 57, 70, 88, 100, 128, 142, 166, 190, 221, 239, 278, 298, 340, 372, 408, 432, 492, 523, 565, 605, 661, 691, 763, 795, 858, 906, 960, 1008, 1099, 1137, 1197, 1253, 1343, 1385, 1481, 1525, 1609, 1687, 1759, 1807, 1931, 1988, 2081, 2153

Offset

0,2

Links

Charles R Greathouse IV, Table of n, a(n) for n = 0..10000

Formula

a(n) = 1 + A024916(n). - R. J. Mathar, May 25 2009

a(n) = 9 + A092406(n) for n>3. - Greg Dresden, Feb 23 2020

Maple

ListTools:-PartialSums(map(numtheory:-sigma, [1, $1..100])); # Robert Israel, Dec 19 2016

Mathematica

lst = {1}; a = 1; Do[a = a + DivisorSigma[1, n]; AppendTo[lst, a], {n, 80}]; lst (* Carl Najafi, Aug 21 2011 *)
Transpose[NestList[{First[#]+1, Last[#]+DivisorSigma[1, First[#]+1]}&, {0, 1}, 50]][[2]] (* Harvey P. Dale, May 05 2012 *)

Prog

(PARI) a(n)=1+sum(k=1, n, sigma(k)) \\ Charles R Greathouse IV, Aug 22 2011
(Python)
from math import isqrt
def A160664(n): return (-(s:=isqrt(n))**2*(s+1) + sum((q:=n//k)*((k<<1)+q+1) for k in range(1, s+1))>>1)+1 # Chai Wah Wu, Oct 22 2023

Crossrefs

Cf. A054519, A092406, A024916. - Greg Dresden, Feb 23 2020

Sequence in context: A045649 A267694 A024519 * A345140 A072829 A169740

Adjacent sequences: A160661 A160662 A160663 * A160665 A160666 A160667

Keyword

nonn

Author

Ctibor O. Zizka, May 22 2009

Extensions

More terms from Carl Najafi, Aug 21 2011

Status

approved