A184387 a(n) = sum of numbers from 1 to sigma(n), where sigma(n) = A000203(n).

1, 6, 10, 28, 21, 78, 36, 120, 91, 171, 78, 406, 105, 300, 300, 496, 171, 780, 210, 903, 528, 666, 300, 1830, 496, 903, 820, 1596, 465, 2628, 528, 2016, 1176, 1485, 1176, 4186, 741, 1830, 1596, 4095, 903, 4656, 990, 3570, 3081, 2628, 1176, 7750, 1653, 4371

Offset: 1

Author

Jaroslav Krizek, Jan 12 2011

Keywords

• nonn

Examples

			For n = 4; sigma(4) = 7; a(4) = 1+2+3+4+5+6+7 = 28.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to sigma(n).

Crossrefs

Cf. A000203, A000217, A002117, A184388, A184389, A184390, A184391, A130674.

Programs

Mathematica

Array[PolygonalNumber@ DivisorSigma[1, #] &, 50] (* Michael De Vlieger, Nov 16 2017 *)

PARI

a(n)=binomial(sigma(n)+1,2) \\ Charles R Greathouse IV, Feb 14 2013

Python

from sympy import divisor_sigma
def A184387(n): return (m:=divisor_sigma(n))*(m+1)>>1 # Chai Wah Wu, Jul 05 2023

Formula

a(n) = Sum_{i = 1..sigma(n)} i = A000217(A000203(n)) = A000203(n)*(A000203(n) + 1)/2.

Sum_{k=1..n} a(k) = (5*zeta(3)/12) * n^3 + O(n^2*log(n)^2). - Amiram Eldar, Dec 08 2022