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 A277608 #13 Sep 11 2024 23:02:07 %S A277608 0,1,2,2,3,3,4,3,4,4,5,4,5,5,5,4,5,5,6,5,6,6,7,5,6,6,6,6,7,6,7,5,6,6, %T A277608 7,6,7,7,7,6,7,7,7,7,7,8,8,6,7,7,7,7,8,7,8,7,8,8,9,7,8,8,8,6,7,7,8,7, %U A277608 8,8,9,7,8,8,8,8,8,8,9,7,8,8,9,8,8,8,9,8 %N A277608 Least number of fractions of the form (k+1)/k, for k a positive integer, whose product equals n. %C A277608 If each intermediate product of the first j of the fractions, for all j < a(n), is also restricted to be an integer, the resulting sequence is A117497. The first n for which a shorter product can be obtained by allowing intermediate non-integer products is 43 = 2/1 * 2/1 * 2/1 * 2/1 * 2/1 * 4/3 * 129/128, a product of 7 fractions, where A117497(43) = 8. %H A277608 Joseph Myers, <a href="/A277608/b277608.txt">Table of n, a(n) for n = 1..10000</a> %H A277608 United Kingdom Mathematics Trust, <a href="https://bmos.ukmt.org.uk/home/ukmog-2016.pdf">Mathematical Olympiad for Girls 2016</a>, problem 5. %Y A277608 Cf. A117497 (restriction to intermediate products being integers), A014701 (always generating n from n-1 for n odd and from n/2 for n even), A376012. %K A277608 nonn %O A277608 1,3 %A A277608 _Joseph Myers_, Oct 23 2016