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

Author

Rémy Sigrist, Oct 15 2019

Keywords

• nonn
• tabf

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).

Examples

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

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program for A328443

Crossrefs

See A328444 for a similar sequence.

Programs

PARI

\\ See Links section.

Formula

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