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The least prime p such that equation x = p*sopf(x) (where sopf(x) is the sum of distinct prime factors of x) has exactly n solutions in positive integers.
5

%I #29 Jan 26 2024 10:19:38

%S 2,3,7,19,71,431,1259,4679,9719,23399,7559,42839,134399,181439,477359,

%T 241919,262079,453599

%N The least prime p such that equation x = p*sopf(x) (where sopf(x) is the sum of distinct prime factors of x) has exactly n solutions in positive integers.

%C It seems that a(n) is the least number for which equation x = p*sopf(x) has exactly n solutions in positive integers not only for prime numbers.

%H Vladimir Letsko, <a href="https://dxdy.ru/post1257616.html#p1257616">Mathematical Marathon, Problem 227</a> (in Russian)

%e a(3) = 7 because there are 3 solutions of the equation x = 7*sopf(x), which are {49, 84, 105}, and this is the smallest prime that gives 3 solutions.

%Y Cf. A008472, A089352, A336098, A336099, A336297, A157190 (note overlap of values).

%K nonn,more

%O 1,1

%A _Vladimir Letsko_, Jul 16 2020