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

1,1

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.

Links

Table of n, a(n) for n=1..18.

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

Example

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.

Crossrefs

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

Sequence in context: A337187 A358049 A025563 * A224929 A110887 A065060

Adjacent sequences: A336293 A336294 A336295 * A336297 A336298 A336299

Keyword

nonn,more

Author

Vladimir Letsko, Jul 16 2020

Status

approved