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%I #11 Jun 30 2020 07:06:23
%S 1,2,36,3489,24778899,566677899999,47777778999999999999
%N Smallest number of multiplicative-additive divisors persistence n.
%C 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.
%C 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.
%e The multiplicative additive divisors persistence of 24778899 is 4: 24778899 -> (2032128/54=) 37632 -> (756/21=) 36 -> (18/9=) 2 -> (2/2=) 1.
%Y Cf. A038367, A126789, A003001, A006050, A007953, A007954, A031346.
%K nonn,base,more
%O 0,2
%A _Pieter Post_, Sep 21 2018
%E Offset set to 0. - _R. J. Mathar_, Jun 30 2020