A357417 Row sums of the triangular array A357431.

1, 5, 12, 27, 43, 76, 109, 168, 218, 301, 383, 499, 591, 779, 904, 1153, 1322, 1555, 1817, 2143, 2379, 2790, 3164, 3627, 3957, 4546, 5034, 5599, 6062, 6937, 7456, 8369, 8973, 9896, 10678, 11663, 12430, 13732, 14618, 15920, 16996, 18471, 19570, 20934, 22189, 24080

Offset: 1

Author

Tamas Sandor Nagy, Sep 27 2022

Keywords

• nonn

Comments

The rows of the triangular array A357431 are chains of numbers that end with the positive terms of A007952.

It appears that lim_{n->oo} a(n)/A002411(n) will converge to a number close to 0.464401.. . - Thomas Scheuerle, Sep 27 2022

Examples

			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.
		

Crossrefs

Cf. A357431, A002411.

Programs

MATLAB

function a = A357417( max_n )
    for n = 1:max_n
        k = [n:-1:1];
        for m = 2:length(k)
            k(m) = k(m)*(floor(k(m-1)/k(m))+1);
        end
        a(n) = sum(k);
    end
end % Thomas Scheuerle, Sep 27 2022

Mathematica

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 *)

PARI

a(n) = my(t=0); sum(k=0,n-1, t++; t+=(-t)%(n-k)); \\ Kevin Ryde, Sep 27 2022