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

%I A143236 #17 Sep 12 2024 11:52:07
%S A143236 1,6,10,24,20,56,32,80,69,108,58,210,74,164,180,250,104,348,120,396,
%T A143236 280,296,152,672,261,364,380,606,206,888,226,714,492,508,524,1260,284,
%U A143236 584,600,1264,320,1344,340,1056,1092,744,376,1980,603,1242,844,1302,438,1816,924
%N A143236 a(n) = A000005(n) * A006218(n).
%H A143236 Robert Israel, <a href="/A143236/b143236.txt">Table of n, a(n) for n = 1..10000</a>
%F A143236 a(n) = Sum_{k=1..n} A143235(n,k).
%e A143236 a(4) = 24 = A000005(4) * A006218(4) = 3*8.
%e A143236 a(4) = 24 = sum of row 4 terms of triangle A143235: (3 + 6 + 6 + 9).
%t A143236 A143236[n_]:= DivisorSigma[0,n]*Sum[Floor[n/k], {k,n}];
%t A143236 Table[A143236[n], {n,100}] (* _G. C. Greubel_, Sep 12 2024 *)
%o A143236 (PARI) A006218(n)=sum(k=1, sqrtint(n), n\k)*2-sqrtint(n)^2
%o A143236 a(n)=A006218(n)*numdiv(n) \\ _Charles R Greathouse IV_, Nov 03 2021
%o A143236 (Python)
%o A143236 from math import isqrt
%o A143236 from sympy import divisor_count
%o A143236 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
%o A143236 (Magma)
%o A143236 A143236:= func< n | NumberOfDivisors(n)*(&+[Floor(n/k): k in [1..n]]) >;
%o A143236 [A143236(n): n in [1..100] ]; // _G. C. Greubel_, Sep 12 2024
%o A143236 (SageMath)
%o A143236 def A143236(n): return sigma(n,0)*sum(int(n//k) for k in range(1,n+1))
%o A143236 [A143236(n) for n in range(1,101)] # _G. C. Greubel_, Sep 12 2024
%Y A143236 Row sums of triangle A143235.
%Y A143236 Cf. A000005, A006218, A143235.
%K A143236 nonn
%O A143236 1,2
%A A143236 _Gary W. Adamson_, Aug 01 2008
%E A143236 More terms from _N. J. A. Sloane_, Oct 19 2008