A143236 a(n) = A000005(n) * A006218(n).

1, 6, 10, 24, 20, 56, 32, 80, 69, 108, 58, 210, 74, 164, 180, 250, 104, 348, 120, 396, 280, 296, 152, 672, 261, 364, 380, 606, 206, 888, 226, 714, 492, 508, 524, 1260, 284, 584, 600, 1264, 320, 1344, 340, 1056, 1092, 744, 376, 1980, 603, 1242, 844, 1302, 438, 1816, 924

Offset: 1

Author

Gary W. Adamson, Aug 01 2008

Keywords

• nonn

Examples

			a(4) = 24 = A000005(4) * A006218(4) = 3*8.
a(4) = 24 = sum of row 4 terms of triangle A143235: (3 + 6 + 6 + 9).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Row sums of triangle A143235.

Cf. A000005, A006218, A143235.

Programs

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

Mathematica

A143236[n_]:= DivisorSigma[0,n]*Sum[Floor[n/k], {k,n}];
Table[A143236[n], {n,100}] (* G. C. Greubel, Sep 12 2024 *)

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

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

Formula

a(n) = Sum_{k=1..n} A143235(n,k).

Extensions

More terms from N. J. A. Sloane, Oct 19 2008