A389591 Sum of the divisors r of n such that r is not greater than twice the adjacent previous divisor of n.

0, 2, 0, 6, 0, 11, 0, 14, 0, 12, 0, 27, 0, 16, 5, 30, 0, 38, 0, 41, 0, 24, 0, 59, 0, 28, 0, 55, 0, 71, 0, 62, 0, 36, 7, 90, 0, 40, 0, 89, 0, 95, 0, 72, 29, 48, 0, 123, 0, 62, 0, 84, 0, 119, 0, 119, 0, 60, 0, 167, 0, 64, 9, 126, 0, 143, 0, 108, 0, 103, 0, 194, 0, 76, 30

Offset

1,2

Comments

Sum of the divisors of n except the smallest numbers of the 2-dense sublists of divisors of n.

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Formula

a(n) = A000203(n) - A379379(n). (Conjectured).

Example

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. The sum of the numbers that are not the smallest number in the second sublist is 26 + 39 + 78 = 143. The total sum is 11 + 143 = 154, so a(78) = 154.

Mathematica

A389591[n_] := Total[Map[Rest, Split[Divisors[n], #2 <= 2*# &]], 2];
Array[A389591, 100] (* Paolo Xausa, Oct 21 2025 *)

Prog

(PARI) a(n) = my(d=divisors(n)); sum(k=1, #d, if ((k>1) && (d[k]<=2*d[k-1]), d[k])); \\ Michel Marcus, Oct 09 2025

Crossrefs

Row sums of A389592.

Cf. A000203, A237271, A384149, A384222, A384226, A384930, A379288, A379379.

Sequence in context: A304439 A266537 A328337 * A285782 A285538 A293935

Adjacent sequences: A389588 A389589 A389590 * A389592 A389593 A389594

Keyword

nonn

Author

Omar E. Pol, Oct 08 2025

Extensions

Extra 0 removed by Sean A. Irvine, Oct 16 2025

a(53) = 0 added and more terms from Paolo Xausa, Oct 21 2025

Status

approved