A376864 4-brilliant numbers with distinct prime factors.

210, 46189, 55913, 62491, 70499, 75361, 78793, 81719, 84227, 89947, 95381, 96577, 99671, 100529, 101959, 103037, 104533, 110143, 111397, 114257, 116831, 121693, 121771, 124729, 127699, 128557, 128843, 130169, 131461, 133331, 134849, 139403, 141427, 143429

Offset: 1

Author

Paul Duckett, Oct 07 2024

Keywords

• nonn
• base
• easy

Examples

			210 = 2*3*5*7 is a term.
130169 = 13*17*19*31 is a term.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A046386 and A376704.

Programs

Python

from sympy import factorint
def ok(n):
    f = factorint(n)
    return len(f) == sum(f.values()) == 4 and len(set([len(str(p)) for p in f])) == 1
print([k for k in range(144000) if ok(k)]) # Michael S. Branicky, Oct 08 2024

Python

from math import prod
from sympy import primerange
from itertools import count, combinations, islice
def bgen(d): # generator of terms that are products of d-digit primes
    primes, out = list(primerange(10**(d-1), 10**d)), set()
    for t in combinations(primes, 4): out.add(prod(t))
    yield from sorted(out)
def agen(): # generator of terms
    for d in count(1): yield from bgen(d)
print(list(islice(agen(), 34))) # Michael S. Branicky, Oct 08 2024

Extensions

Terms corrected by Michael S. Branicky, Oct 08 2024