A143236 - OEIS

%I #17 Sep 12 2024 11:52:07

%S 1,6,10,24,20,56,32,80,69,108,58,210,74,164,180,250,104,348,120,396,

%T 280,296,152,672,261,364,380,606,206,888,226,714,492,508,524,1260,284,

%U 584,600,1264,320,1344,340,1056,1092,744,376,1980,603,1242,844,1302,438,1816,924

%N a(n) = A000005(n) * A006218(n).

%H Robert Israel, <a href="/A143236/b143236.txt">Table of n, a(n) for n = 1..10000</a>

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

%e a(4) = 24 = A000005(4) * A006218(4) = 3*8.

%e a(4) = 24 = sum of row 4 terms of triangle A143235: (3 + 6 + 6 + 9).

%t A143236[n_]:= DivisorSigma[0,n]*Sum[Floor[n/k], {k,n}];

%t Table[A143236[n], {n,100}] (* _G. C. Greubel_, Sep 12 2024 *)

%o (PARI) A006218(n)=sum(k=1, sqrtint(n), n\k)*2-sqrtint(n)^2

%o a(n)=A006218(n)*numdiv(n) \\ _Charles R Greathouse IV_, Nov 03 2021

%o (Python)

%o from math import isqrt

%o from sympy import divisor_count

%o 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 (Magma)

%o A143236:= func< n | NumberOfDivisors(n)*(&+[Floor(n/k): k in [1..n]]) >;

%o [A143236(n): n in [1..100] ]; // _G. C. Greubel_, Sep 12 2024

%o (SageMath)

%o def A143236(n): return sigma(n,0)*sum(int(n//k) for k in range(1,n+1))

%o [A143236(n) for n in range(1,101)] # _G. C. Greubel_, Sep 12 2024

%Y Row sums of triangle A143235.

%Y Cf. A000005, A006218, A143235.

%K nonn

%O 1,2

%A _Gary W. Adamson_, Aug 01 2008

%E More terms from _N. J. A. Sloane_, Oct 19 2008