A062822 Sum of divisors of the squarefree numbers: sigma(A005117(n)).

1, 3, 4, 6, 12, 8, 18, 12, 14, 24, 24, 18, 20, 32, 36, 24, 42, 30, 72, 32, 48, 54, 48, 38, 60, 56, 42, 96, 44, 72, 48, 72, 54, 72, 80, 90, 60, 62, 96, 84, 144, 68, 96, 144, 72, 74, 114, 96, 168, 80, 126, 84, 108, 132, 120, 90, 112, 128, 144, 120, 98, 102, 216, 104, 192

Offset: 1

Author

Jason Earls, Jul 20 2001

Keywords

• nonn

Links

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

Crossrefs

Cf. A000203, A005117, A002117, A152649, A265668, A001221.

Programs

Haskell

a062822 1 = 1
a062822 n = product $ map (+ 1) $ a265668_row n
-- Reinhard Zumkeller, Dec 13 2015

Mathematica

DivisorSigma[1,#]&/@Select[Range[150],SquareFreeQ] (* Harvey P. Dale, May 18 2014 *)

PARI

j=[]; for(n=1,200, if(issquarefree(n),j=concat(j, sigma(n)))); j

Python

from math import isqrt
from sympy import mobius, divisor_sigma
def A062822(n):
    def f(x): return n+x-sum(mobius(k)*(x//k**2) for k in range(1, isqrt(x)+1))
    m, k = n, f(n)
    while m != k:
        m, k = k, f(k)
    return divisor_sigma(m) # Chai Wah Wu, Aug 12 2024

Formula

a(n) = Product_{k=1..A001221(n)} (A265668(n,k) + 1). - Reinhard Zumkeller, Dec 13 2015

From Amiram Eldar, Nov 21 2022: (Start)

a(n) = A000203(A005117(n)).

Sum_{k=1..n} a(k) ~ c * n^2, where c = Pi^4/(72*zeta(3)) = A152649 / A002117 = 1.1254908... . (End)