A355441 Numbers k such that the sum of the least prime factors of i=2..k is prime.

2, 3, 4, 8, 12, 15, 16, 20, 24, 40, 43, 52, 55, 60, 63, 68, 72, 79, 87, 95, 96, 108, 111, 120, 123, 136, 140, 148, 151, 160, 184, 211, 215, 216, 227, 232, 235, 239, 252, 255, 256, 260, 264, 280, 283, 288, 299, 307, 323, 324, 327, 332, 360, 363, 371, 372, 375, 379

Offset: 1

Author

Jean-Marc Rebert, Jul 02 2022

Keywords

• nonn

Examples

			8 is a term since the least prime factors of 2..8 are 2, 3, 2, 5, 2, 7, 2 and their sum 23 is prime.
		

Links

• Jean-Marc Rebert, Table of n, a(n) for n = 1..5676

Crossrefs

Cf. A088821.

Programs

Mathematica

Position[Accumulate[Join[{0}, Table[FactorInteger[k][[1, 1]], {k, 2, 400}]]], ?PrimeQ] // Flatten (* _Amiram Eldar, Jul 02 2022 *)

PARI

isok(k) = isprime(sum(i=2, k, factor(i)[1,1])); \\ Michel Marcus, Jul 04 2022

Python

from sympy import isprime, factorint
from itertools import accumulate, count, islice
def agen(): yield from (k for k, sk in enumerate(accumulate(min(factorint(i)) for i in count(2)), 2) if isprime(sk))
print(list(islice(agen(), 75))) # Michael S. Branicky, Jul 02 2022