A277608 Least number of fractions of the form (k+1)/k, for k a positive integer, whose product equals n.

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, 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, 8, 8, 9, 7, 8, 8, 8, 8, 8, 8, 9, 7, 8, 8, 9, 8, 8, 8, 9, 8

Offset: 1

Author

Joseph Myers, Oct 23 2016

Keywords

• nonn

Comments

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.

Links

• Joseph Myers, Table of n, a(n) for n = 1..10000
• United Kingdom Mathematics Trust, Mathematical Olympiad for Girls 2016, problem 5.

Crossrefs

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.