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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.
2
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
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: A372031 A225642 A273317 * A122866 A097275 A130879
KEYWORD
nonn,tabf
AUTHOR
Rémy Sigrist, Oct 15 2019
STATUS
approved