A184390 a(n) = sum of numbers from 1 to pi(n), where pi(n) = A007955(n).

1, 3, 6, 36, 15, 666, 28, 2080, 378, 5050, 66, 1493856, 91, 19306, 25425, 524800, 153, 17009028, 190, 32004000, 97461, 117370, 276, 55037822976, 7875, 228826, 266085, 240956128, 435, 328050405000

Offset: 1

Author

Jaroslav Krizek, Jan 12 2011

Keywords

• nonn

Examples

			For n = 6; pi(6) = 36; a(n) = (1/2)*36*37 = 666.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A184387, A184388, A184389, A184391, A130674.

Programs

Mathematica

# (#+1)/2&/@Array[Times@@Divisors[#]&,40] (* Harvey P. Dale, Oct 05 2012 *)

Python

from math import isqrt
from sympy import divisor_count
def A184390(n): return (m:=((isqrt(n) if (c:=divisor_count(n)) & 1 else 1)*n**(c//2)))*(m+1)//2 # Chai Wah Wu, Jun 25 2022

Formula

a(n) = Sum_{i = 1..pi(n)} i = A000217(A007955(n)) = (1/2)*A007955(n)*(A007955(n)+1).