cp's OEIS Frontend

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

%I A184387 #31 Jul 06 2023 01:51:07
%S A184387 1,6,10,28,21,78,36,120,91,171,78,406,105,300,300,496,171,780,210,903,
%T A184387 528,666,300,1830,496,903,820,1596,465,2628,528,2016,1176,1485,1176,
%U A184387 4186,741,1830,1596,4095,903,4656,990,3570,3081,2628,1176,7750,1653,4371
%N A184387 a(n) = sum of numbers from 1 to sigma(n), where sigma(n) = A000203(n).
%H A184387 Antti Karttunen, <a href="/A184387/b184387.txt">Table of n, a(n) for n = 1..10000</a>
%H A184387 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.
%F A184387 a(n) = Sum_{i = 1..sigma(n)} i = A000217(A000203(n)) = A000203(n)*(A000203(n) + 1)/2.
%F A184387 Sum_{k=1..n} a(k) = (5*zeta(3)/12) * n^3 + O(n^2*log(n)^2). - _Amiram Eldar_, Dec 08 2022
%e A184387 For n = 4; sigma(4) = 7; a(4) = 1+2+3+4+5+6+7 = 28.
%t A184387 Array[PolygonalNumber@ DivisorSigma[1, #] &, 50] (* _Michael De Vlieger_, Nov 16 2017 *)
%o A184387 (PARI) a(n)=binomial(sigma(n)+1,2) \\ _Charles R Greathouse IV_, Feb 14 2013
%o A184387 (Python)
%o A184387 from sympy import divisor_sigma
%o A184387 def A184387(n): return (m:=divisor_sigma(n))*(m+1)>>1 # _Chai Wah Wu_, Jul 05 2023
%Y A184387 Cf. A000203, A000217, A002117, A184388, A184389, A184390, A184391, A130674.
%K A184387 nonn
%O A184387 1,2
%A A184387 _Jaroslav Krizek_, Jan 12 2011