A319507 Smallest number of multiplicative-additive divisors persistence n.

1, 2, 36, 3489, 24778899, 566677899999, 47777778999999999999

Offset: 0

Author

Pieter Post, Sep 21 2018

Keywords

• nonn
• base
• more

Comments

To compute the "multiplicative-additive divisors persistence" of a number, we proceed as follows. Form the product of the digits of the number (A007954) divided by the sum of the digits (A007953). Repeat this process until you reach 0 or 1. If we reach a non-integer, we write 0. The "multiplicative-additive divisors persistence" is the number of steps to reach 0 or 1.

For instance: the multiplicative-additive divisors persistence of 874 is 1, because 874 -> 8 * 7 * 4 / (8 + 7 + 4) = 224/19. This is not an integer, so the process stops after one step.

Examples

			The multiplicative additive divisors persistence of 24778899 is 4: 24778899 -> (2032128/54=) 37632 -> (756/21=) 36 -> (18/9=) 2 -> (2/2=) 1.
		

Crossrefs

Cf. A038367, A126789, A003001, A006050, A007953, A007954, A031346.

Extensions

Offset set to 0. - R. J. Mathar, Jun 30 2020