A336296 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.

2, 3, 7, 19, 71, 431, 1259, 4679, 9719, 23399, 7559, 42839, 134399, 181439, 477359, 241919, 262079, 453599

Offset: 1

Author

Vladimir Letsko, Jul 16 2020

Keywords

• nonn
• more

Comments

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.

Examples

			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.
		

Links

• Vladimir Letsko, Mathematical Marathon, Problem 227 (in Russian)

Crossrefs

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