A389592 - OEIS

A389592

Irregular triangle read by rows: T(n,k) is the sum of the numbers that are not the smallest number in the k-th 2-dense sublist of divisors of n, with n >= 1, k >= 1.

0, 2, 0, 0, 6, 0, 0, 11, 0, 0, 14, 0, 0, 0, 2, 10, 0, 0, 27, 0, 0, 2, 14, 0, 5, 0, 30, 0, 0, 38, 0, 0, 41, 0, 0, 0, 0, 2, 22, 0, 0, 59, 0, 0, 0, 2, 26, 0, 0, 0, 0, 55, 0, 0, 71, 0, 0, 62, 0, 0, 0, 0, 2, 34, 0, 7, 0, 90, 0, 0, 2, 38, 0, 0, 0, 0, 89, 0, 0, 95, 0, 0, 6, 66, 0, 29, 0, 2, 46, 0, 0, 123

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OFFSET

1,2

LINKS

Paolo Xausa, Table of n, a(n) for n = 1..12242 (rows 1..4000 of triangle, flattened).

FORMULA

Conjecture: T(n,k) = A384149(n,k) - A379288(n,k).

EXAMPLE

Triangle begins:

0, 0;

11;

0, 0;

14;

0, 0, 0;

2, 10;

0, 0;

27;

0, 0;

2, 14;

0, 5, 0;

30;

...

For n = 78 the list of divisors of 78 is [1, 2, 3, 6, 13, 26, 39, 78]. There are two 2-dense sublists of divisors of 78, they are [1, 2, 3, 6] and [13, 26, 39, 78]. The sum of the numbers that are not the smallest number in the first sublist is 2 + 3 + 6 = 11, so T(78, 1) = 11. The sum of the numbers that are not the smallest number in the second sublist is 26 + 39 + 78 = 143, so T(78, 2) = 143.

MATHEMATICA

A389592row[n_] := Map[Total[Rest[#]] &, Split[Divisors[n], #2 <= 2*# &]];

Array[A389592row, 50] (* Paolo Xausa, Oct 21 2025 *)

CROSSREFS

Row sums give A389591.

Cf. A237271, A384149, A384222, A384226, A384930, A379288, A379379.

Sequence in context: A094785 A390443 A265856 * A035536 A205974 A098643

Adjacent sequences: A389589 A389590 A389591 * A389593 A389594 A389595

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Oct 08 2025

STATUS

approved