This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A329549 #23 Nov 17 2019 15:56:18 %S A329549 8,24,40,56,64,120,144,280,320,448,704,720,832,1008,1024,1152,2240, %T A329549 3200,4928,5040,5760,5824,6272,8064,9152,10368,11264,13312,17408, %U A329549 19456,22400,23552,29696,31744,32768,35200,40320,41600,51200,51840,64064,68992,72576,81536,100352,114048 %N A329549 Numbers 4*k such that 1 is the last integer obtained when 4*k is successively divided by its divisors in increasing order. %C A329549 At sequence A076933, the question is asked: "What is the longest string of ones in this sequence?" As A076933(4*n) is rarely 1, such a string is not very long. The longest starting below 4*10^8 has length 6 and starts at 141. Checking multiples of 4 may help in finding longer such strings. %C A329549 Terms are also a multiple of 8. Proof: If m = 8*k + 4 then its divisors are 1, 2, 4 (and maybe 3). After dividing by 4 we have a fraction with denominator 2. Before that we did not see 1. %e A329549 The divisors of 8 are 1, 2, 4 and 8. Dividing from left to right gives 8/1 = 8, 8/2 = 4, 4/4 = 1, and then 1/8 isn't an integer so as the last integer we see is 1, 8 is in the sequence. %Y A329549 Cf. A076933, A240694 (partial products of divisors of n). %Y A329549 Subsequence of A008586 (multiples of 4) and of A008590 (multiples of 8). %K A329549 nonn %O A329549 1,1 %A A329549 _David A. Corneth_, Nov 16 2019