A143238 a(n) = A000203(n) * A024916(n).

1, 12, 32, 105, 126, 396, 328, 840, 897, 1566, 1188, 3556, 1974, 3960, 4536, 6820, 4284, 10803, 5940, 14238, 11872, 14652, 10344, 29460, 16182, 23688, 24160, 36960, 20700, 54864, 25408, 53991, 43440, 51786, 48336, 99918, 43168, 71760, 70112, 120780, 58128, 142080

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Formula

a(n) = A000203(n) * A024916(n).

a(n) = Sum_{k=1..n} A143237(n, k).

Example

a(4) = 105 = A000203(4) * A024916(4) = 7 * 15.
a(4) = 105 = sum of row 4 terms of triangle A143237: (7, + 21, + 28 + 49).

Mathematica

sigma = Table[DivisorSigma[1, n], {n, 1, 50}]; sigma * Accumulate[sigma] (* Amiram Eldar, Feb 26 2020 *)

Prog

(Python)
from math import isqrt
from sympy import divisor_sigma
def A143238(n): return (-(s:=isqrt(n))**2*(s+1) + sum((q:=n//k)*((k<<1)+q+1) for k in range(1, s+1))>>1)*divisor_sigma(n) # Chai Wah Wu, Oct 23 2023
(Magma)
A143238:= func< n | DivisorSigma(1, n)*(&+[k*Floor(n/k): k in [1..n]]) >;
[A143238(n): n in [1..100]]; // G. C. Greubel, Sep 12 2024
(SageMath)
def A143238(n): return sigma(n, 1)*sum(k*int(n//k) for k in range(1, n+1))
[A143238(n) for n in range(1, 101)] # G. C. Greubel, Sep 12 2024

Crossrefs

Cf. A000203, A024916, A143237.

Sequence in context: A242543 A194644 A068381 * A102091 A303079 A268769

Adjacent sequences: A143235 A143236 A143237 * A143239 A143240 A143241

Keyword

nonn

Author

Gary W. Adamson, Aug 01 2008

Extensions

More terms from Amiram Eldar, Feb 26 2020

Status

approved