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

1,2

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

Links

Table of n, a(n) for n=1..46.

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A357431, A002411.

Sequence in context: A176448 A078517 A170828 * A229422 A128439 A240187

Adjacent sequences: A357414 A357415 A357416 * A357418 A357419 A357420

Keyword

nonn

Author

Tamas Sandor Nagy, Sep 27 2022

Status

approved