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

1,3

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).

Sequence in context: A137813 A003313 A353058 * A117497 A117498 A064097

Adjacent sequences: A277605 A277606 A277607 * A277609 A277610 A277611

Keyword

nonn

Author

Joseph Myers, Oct 23 2016

Status

approved