A328443 Lexicographically earliest sequence of distinct positive numbers such that a(1) = 1, a(2) = 2, and for n > 2, a(n) divides Sum_{i = 1..k} a(i) with k > 0 as small as possible.

1, 2, 3, 6, 4, 12, 8, 16, 7, 14, 28, 9, 18, 36, 13, 26, 52, 59, 73, 101, 5, 10, 11, 22, 55, 110, 32, 64, 128, 41, 82, 164, 177, 29, 203, 15, 17, 51, 85, 255, 157, 314, 43, 129, 387, 61, 122, 244, 488, 493, 503, 257, 514, 67, 134, 268, 536, 197, 591, 701, 733

Offset

1,2

Comments

When computing a(n) for n > 2, there may be candidates for different values of k; we choose the candidate that minimizes k.

This sequence can also be seen as an irregular table, with first row (1, 2), and for n > 1, the n-th row corresponds to the divisors of the sum of the first n terms not yet in the sequence in ascending order (and the sum of the first n terms is the last term of the n-th row).

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, PARI program for A328443

Formula

a(n) <= Sum_{k = 1..n-1} a(k) for any n > 2.

Example

The table begins:
     1, 2;
     3;
     6;
     4, 12;
     8, 16;
     7, 14, 28;
     9, 18, 36;
     ...

Prog

(PARI) See Links section.

Crossrefs

See A328444 for a similar sequence.

Sequence in context: A046202 A225642 A273317 * A122866 A097275 A130879

Adjacent sequences: A328440 A328441 A328442 * A328444 A328445 A328446

Keyword

nonn,tabf

Author

Rémy Sigrist, Oct 15 2019

Status

approved