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URL: https://oeis.org/A062822

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A062822
Sum of divisors of the squarefree numbers: sigma(A005117(n)).
10
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
1,2
LINKS
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)
MATHEMATICA
DivisorSigma[1, #]&/@Select[Range[150], SquareFreeQ] (* Harvey P. Dale, May 18 2014 *)
PROG
(PARI) j=[]; for(n=1, 200, if(issquarefree(n), j=concat(j, sigma(n)))); j
(Haskell)
a062822 1 = 1
a062822 n = product $ map (+ 1) $ a265668_row n
-- Reinhard Zumkeller, Dec 13 2015
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Jason Earls, Jul 20 2001
STATUS
approved