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A357417 Row sums of the triangular array A357431.

%I A357417 #38 Nov 20 2022 05:54:38
%S A357417 1,5,12,27,43,76,109,168,218,301,383,499,591,779,904,1153,1322,1555,
%T A357417 1817,2143,2379,2790,3164,3627,3957,4546,5034,5599,6062,6937,7456,
%U A357417 8369,8973,9896,10678,11663,12430,13732,14618,15920,16996,18471,19570,20934,22189,24080
%N A357417 Row sums of the triangular array A357431.
%C A357417 The rows of the triangular array A357431 are chains of numbers that end with the positive terms of A007952.
%C A357417 It appears that lim_{n->oo} a(n)/A002411(n) will converge to a number close to 0.464401.. . - _Thomas Scheuerle_, Sep 27 2022
%e A357417 For n = 6, the numbers of the chain that are divisible by 6, 5, 4, 3, 2, and 1 are 6, 10, 12, 15, 16, and 17, these forming row 6 of A357431. The sum of this row is a(6) = 76.
%t A357417 a[n_] := Module[{k = n, s = n, r}, Do[k++; k += If[(r = Mod[k, i]) == 0, 0, i - Mod[k, i]]; s += k, {i, n - 1, 1, -1}]; s]; Array[a, 50] (* _Amiram Eldar_, Sep 27 2022 *)
%o A357417 (MATLAB)
%o A357417 function a = A357417( max_n )
%o A357417     for n = 1:max_n
%o A357417         k = [n:-1:1];
%o A357417         for m = 2:length(k)
%o A357417             k(m) = k(m)*(floor(k(m-1)/k(m))+1);
%o A357417         end
%o A357417         a(n) = sum(k);
%o A357417     end
%o A357417 end % _Thomas Scheuerle_, Sep 27 2022
%o A357417 (PARI) a(n) = my(t=0); sum(k=0,n-1, t++; t+=(-t)%(n-k)); \\ _Kevin Ryde_, Sep 27 2022
%Y A357417 Cf. A357431, A002411.
%K A357417 nonn
%O A357417 1,2
%A A357417 _Tamas Sandor Nagy_, Sep 27 2022