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A066353 1 + partial sums of A032378.

%I A066353 #16 Jan 25 2025 13:46:00
%S A066353 1,3,6,10,15,21,28,38,50,64,80,98,118,140,164,190,220,253,289,328,370,
%T A066353 415,463,514,568,625,685,748,816,888,964,1044,1128,1216,1308,1404,
%U A066353 1504,1608,1716,1828,1944,2064,2188,2318,2453,2593,2738,2888
%N A066353 1 + partial sums of A032378.
%C A066353 A032378 has been inspired by the Concrete Mathematics Casino problem (see reference).
%D A066353 R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. 2nd Edition. Addison-Wesley, Reading, MA, 1994. Section 3.2, p74-76.
%H A066353 G. C. Greubel, <a href="/A066353/b066353.txt">Table of n, a(n) for n = 0..10000</a>
%F A066353 a(n) = 1 if n = 0, otherwise a(n) = A112873(n) = Sum_{j=1..n} A032378(j).
%t A066353 A032378:= A032378= Table[k*j, {k,15}, {j,k^2+1, k^2+3*k+3}]//Flatten;
%t A066353 A066353[n_]:= A066353[n]= 1 +Sum[A032378[[j+1]], {j,0,n-1}];
%t A066353 Table[A066353[n], {n,0,100}] (* _G. C. Greubel_, Jul 20 2023 *)
%t A066353 Accumulate[Join[{1},Select[Range[300],!IntegerQ[Surd[#,3]]&&Divisible[#,Floor[Surd[#,3]]]&]]] (* _Harvey P. Dale_, Jan 25 2025 *)
%o A066353 (Magma)
%o A066353 A032378:=[k*j: j in [(k^2+1)..(k^2+3*k+3)], k in [1..15]];
%o A066353 [n eq 0 select 1 else 1+(&+[A032378[j]: j in [1..n]]): n in [0..100]]; // _G. C. Greubel_, Jul 20 2023
%o A066353 (SageMath)
%o A066353 A032378=flatten([[k*j for j in range((k^2+1),(k^2+3*k+3)+1)] for k in range(1,15)])
%o A066353 def A066353(n): return 1 if (n==0) else 1 + sum(A032378[j] for j in range(n))
%o A066353 [A066353(n) for n in range(101)] # _G. C. Greubel_, Jul 20 2023
%Y A066353 Cf. A032378, A112873.
%K A066353 nonn
%O A066353 0,2
%A A066353 _N. J. A. Sloane_, Dec 22 2001