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

1,2

Links

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

Formula

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

Example

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

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

Row sums of triangle A143235.

Cf. A000005, A006218, A143235.

Sequence in context: A132994 A199885 A024499 * A107306 A108899 A074289

Adjacent sequences: A143233 A143234 A143235 * A143237 A143238 A143239

Keyword

nonn,changed

Author

Gary W. Adamson, Aug 01 2008

Extensions

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

Status

approved