The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #23 Nov 17 2019 15:56:18
%S 8,24,40,56,64,120,144,280,320,448,704,720,832,1008,1024,1152,2240,
%T 3200,4928,5040,5760,5824,6272,8064,9152,10368,11264,13312,17408,
%U 19456,22400,23552,29696,31744,32768,35200,40320,41600,51200,51840,64064,68992,72576,81536,100352,114048
%N Numbers 4*k such that 1 is the last integer obtained when 4*k is successively divided by its divisors in increasing order.
%C 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 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 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 Cf. A076933, A240694 (partial products of divisors of n).
%Y Subsequence of A008586 (multiples of 4) and of A008590 (multiples of 8).
%K nonn
%O 1,1
%A _David A. Corneth_, Nov 16 2019