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

%I A143238 #14 Sep 12 2024 11:45:58
%S A143238 1,12,32,105,126,396,328,840,897,1566,1188,3556,1974,3960,4536,6820,
%T A143238 4284,10803,5940,14238,11872,14652,10344,29460,16182,23688,24160,
%U A143238 36960,20700,54864,25408,53991,43440,51786,48336,99918,43168,71760,70112,120780,58128,142080
%N A143238 a(n) = A000203(n) * A024916(n).
%H A143238 G. C. Greubel, <a href="/A143238/b143238.txt">Table of n, a(n) for n = 1..10000</a>
%F A143238 a(n) = A000203(n) * A024916(n).
%F A143238 a(n) = Sum_{k=1..n} A143237(n, k).
%e A143238 a(4) = 105 = A000203(4) * A024916(4) = 7 * 15.
%e A143238 a(4) = 105 = sum of row 4 terms of triangle A143237: (7, + 21, + 28 + 49).
%t A143238 sigma = Table[DivisorSigma[1, n], {n, 1, 50}]; sigma * Accumulate[sigma] (* _Amiram Eldar_, Feb 26 2020 *)
%o A143238 (Python)
%o A143238 from math import isqrt
%o A143238 from sympy import divisor_sigma
%o A143238 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
%o A143238 (Magma)
%o A143238 A143238:= func< n | DivisorSigma(1,n)*(&+[k*Floor(n/k): k in [1..n]]) >;
%o A143238 [A143238(n): n in [1..100]]; // _G. C. Greubel_, Sep 12 2024
%o A143238 (SageMath)
%o A143238 def A143238(n): return sigma(n,1)*sum(k*int(n//k) for k in range(1,n+1))
%o A143238 [A143238(n) for n in range(1,101)] # _G. C. Greubel_, Sep 12 2024
%Y A143238 Cf. A000203, A024916, A143237.
%K A143238 nonn
%O A143238 1,2
%A A143238 _Gary W. Adamson_, Aug 01 2008
%E A143238 More terms from _Amiram Eldar_, Feb 26 2020