OFFSET
1,2
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = Sum_{k=1..n} A143235(n,k).
EXAMPLE
MATHEMATICA
A143236[n_]:= DivisorSigma[0, n]*Sum[Floor[n/k], {k, n}];
Table[A143236[n], {n, 100}] (* G. C. Greubel, Sep 12 2024 *)
PROG
(PARI) A006218(n)=sum(k=1, sqrtint(n), n\k)*2-sqrtint(n)^2
a(n)=A006218(n)*numdiv(n) \\ Charles R Greathouse IV, Nov 03 2021
(Python)
from math import isqrt
from sympy import divisor_count
def A143236(n): return (-(s:=isqrt(n))**2+(sum(n//k for k in range(1, s+1))<<1))*divisor_count(n) # Chai Wah Wu, Oct 23 2023
(Magma)
A143236:= func< n | NumberOfDivisors(n)*(&+[Floor(n/k): k in [1..n]]) >;
[A143236(n): n in [1..100] ]; // G. C. Greubel, Sep 12 2024
(SageMath)
def A143236(n): return sigma(n, 0)*sum(int(n//k) for k in range(1, n+1))
[A143236(n) for n in range(1, 101)] # G. C. Greubel, Sep 12 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Gary W. Adamson, Aug 01 2008
EXTENSIONS
More terms from N. J. A. Sloane, Oct 19 2008
STATUS
approved