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 A329549 Numbers 4*k such that 1 is the last integer obtained when 4*k is successively divided by its divisors in increasing order. 1
 8, 24, 40, 56, 64, 120, 144, 280, 320, 448, 704, 720, 832, 1008, 1024, 1152, 2240, 3200, 4928, 5040, 5760, 5824, 6272, 8064, 9152, 10368, 11264, 13312, 17408, 19456, 22400, 23552, 29696, 31744, 32768, 35200, 40320, 41600, 51200, 51840, 64064, 68992, 72576, 81536, 100352, 114048 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. 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. LINKS EXAMPLE 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. CROSSREFS Cf. A076933, A240694 (partial products of divisors of n). Subsequence of A008586 (multiples of 4) and of A008590 (multiples of 8). Sequence in context: A304475 A316300 A050427 * A031046 A173080 A051062 Adjacent sequences:  A329546 A329547 A329548 * A329550 A329551 A329552 KEYWORD nonn AUTHOR David A. Corneth, Nov 16 2019 STATUS approved

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Last modified August 3 17:13 EDT 2021. Contains 346439 sequences. (Running on oeis4.)