cp's OEIS Frontend

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.

%I A328443 #19 Aug 23 2024 15:05:05
%S A328443 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,
%T A328443 110,32,64,128,41,82,164,177,29,203,15,17,51,85,255,157,314,43,129,
%U A328443 387,61,122,244,488,493,503,257,514,67,134,268,536,197,591,701,733
%N 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.
%C A328443 When computing a(n) for n > 2, there may be candidates for different values of k; we choose the candidate that minimizes k.
%C A328443 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).
%H A328443 Rémy Sigrist, <a href="/A328443/b328443.txt">Table of n, a(n) for n = 1..10000</a>
%H A328443 Rémy Sigrist, <a href="/A328443/a328443.gp.txt">PARI program for A328443</a>
%F A328443 a(n) <= Sum_{k = 1..n-1} a(k) for any n > 2.
%e A328443 The table begins:
%e A328443      1, 2;
%e A328443      3;
%e A328443      6;
%e A328443      4, 12;
%e A328443      8, 16;
%e A328443      7, 14, 28;
%e A328443      9, 18, 36;
%e A328443      ...
%o A328443 (PARI) \\ See Links section.
%Y A328443 See A328444 for a similar sequence.
%K A328443 nonn,tabf
%O A328443 1,2
%A A328443 _Rémy Sigrist_, Oct 15 2019