A287820 Least number of factors to express A065108(n) as a product of Fibonacci numbers.

0, 1, 1, 2, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 3, 1, 2, 2, 2, 3, 3, 3, 1, 4, 2, 2, 2, 3, 3, 3, 3, 4, 1, 4, 2, 2, 2, 2, 3, 3, 3, 3, 4, 3, 1, 4, 4, 4, 2, 2, 2, 5, 2, 3, 3, 3, 3, 3, 3, 4, 3, 1, 4, 4, 4, 5, 2, 2, 2, 2, 2, 5, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 1, 4, 4, 5, 4, 4

Offset: 1

Author

David A. Corneth, Jun 01 2017

Keywords

• nonn
• easy
• look

Comments

Some terms of A065108 are a product of Fibonacci numbers in more than one way. For example, 8 is a product of Fibonacci numbers in more than one way as 8 = 2 * 2 * 2 and both 8 and 2 are Fibonacci numbers. Therefore, 'at least' is used in the name.

Examples

			8 = 2 * 2 * 2 are all ways to write A065108(7) = 8 as a product of Fibonacci numbers. 8 has one factor, the least number of all such factorizations. Therefore, a(7) = 1.
81 = 3^4. 81 isn't a Fibonacci number. 3^4 is the only factorization of A065108(43) = 81 into Fibonacci numbers and has four factors 3. Therefore, a(43) = 4.
144 = 2 * 3 * 3 * 8 = 2 * 2 * 2 * 2 * 3 * 3 are all ways to write A065108(62) = 144 as a product of Fibonacci numbers. 144 has one factor, the least number of all such factorizations. Therefore, a(62) = 1.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A065108, A261769, A287821.

Extensions

Name clarified by Chai Wah Wu, Jun 02 2017