A354160 Products of exactly two distinct primes in A090252, in order of appearance.

21, 55, 26, 85, 57, 161, 319, 217, 481, 205, 731, 517, 159, 1121, 1403, 871, 355, 1241, 869, 2407, 1691, 413, 3007, 2323, 206, 1391, 4033, 565, 5207, 2227, 5891, 6533, 4321, 453, 1007, 623, 4867, 2231, 6161, 2119, 11189, 6401, 12709, 7421, 2159, 9563, 8213, 1507, 15247, 9259, 4031, 12367, 597, 2869, 11183, 1561, 13393, 7099, 3611, 14213, 478, 24823

Offset: 1

Author

N. J. A. Sloane, May 30 2022

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..2517
• Michael De Vlieger, Annotated log-log scatterplot of A090252(n), n = 1..2^12, labeling primes in red, highlighting composite prime powers in gold, squarefree semiprimes in green and labeling them in boldface.

Crossrefs

Cf. A090252, A354159, A354161, A354162, A354163.

Programs

Mathematica

Select[Import["https://oeis.org/A090252/b090252.txt", "Data"][[1 ;; 2000, -1]], PrimeNu[#] == PrimeOmega[#] == 2 &] (* Michael De Vlieger, Jun 16 2022 *)

Python

from itertools import count, islice
from collections import deque
from math import gcd, lcm
from sympy import factorint
def A354160_gen(): # generator of terms
    aset, aqueue, c, b, f = {1}, deque([1]), 2, 1, True
    while True:
        for m in count(c):
            if m not in aset and gcd(m,b) == 1:
                if len(fm := factorint(m)) == sum(fm.values()) == 2:
                    yield m
                aset.add(m)
                aqueue.append(m)
                if f: aqueue.popleft()
                b = lcm(*aqueue)
                f = not f
                while c in aset:
                    c += 1
                break
A354160_list = list(islice(A354160_gen(),25)) # Chai Wah Wu, May 31 2022