A389138 Composite numbers not in A387184.

4, 46, 58, 65, 69, 74, 86, 87, 93, 94, 106, 111, 114, 115, 118, 119, 123, 129, 130, 134, 145, 158, 159, 161, 166, 174, 177, 178, 183, 185, 186, 187, 195, 201, 202, 205, 206, 209, 213, 214, 215, 217, 218, 219, 235, 237, 238, 247, 249, 259, 262, 266, 267, 273, 274, 278

Offset

1,1

Comments

The first non-semiprime terms are 114, 130, 174, 186, ... . What is the smallest term with more than 3 prime factors?

First term with 4 prime factors is a(189) = 690. First term with 5 prime factors is a(2625) = 6510. - Chai Wah Wu, Sep 24 2025

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Prog

(Python)
from math import prod
from itertools import count, islice
from sympy import factorint, integer_nthroot, isprime
def A389138_gen(): # generator of terms
    g, p, r = [set()], 0, {}
    for c in count(2):
        f = factorint(c)
        d = g[-1]^set(i for i, j in f.items() if j&1)
        for h in g:
            if (t:=prod(d^h)) not in r:
                r[t] = c-1
        g.append(d)
        x, y = integer_nthroot(c, 2)
        if c>4 and y and isprime(x):
            continue
        elif c>4 and max(f.values())>1:
            continue
        else:
            flag = False
            for b in range(c-2, p, -1):
                e = prod(d^g[b])
                if e in r and r[e]<b:
                    flag = True
                    break
            if flag:
                continue
        if isprime(c):
            p = c-2
        else:
            yield c
A389138_list = list(islice(A389138_gen(), 56)) # Chai Wah Wu, Sep 24 2025, updated Oct 05 2025

Crossrefs

Cf. A387184 (see there for more information).

Sequence in context: A349866 A222899 A119729 * A374591 A134110 A384584

Adjacent sequences: A389135 A389136 A389137 * A389139 A389140 A389141

Keyword

nonn

Author

Hugo Pfoertner, Sep 24 2025

Status

approved