A333964 Numbers of the form 2^i * 6^j * 30^k * 210^m where i, j, k, m >= 0.

1, 2, 4, 6, 8, 12, 16, 24, 30, 32, 36, 48, 60, 64, 72, 96, 120, 128, 144, 180, 192, 210, 216, 240, 256, 288, 360, 384, 420, 432, 480, 512, 576, 720, 768, 840, 864, 900, 960, 1024, 1080, 1152, 1260, 1296, 1440, 1536, 1680, 1728, 1800, 1920, 2048, 2160, 2304, 2520, 2592

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

Sum_{n>=1} 1/a(n) = 15120/6061. - Amiram Eldar, Feb 18 2021

Mathematica

mx = 2600; Select[Sort[Flatten[Table[2^i*6^j*30^k*210^m, {i, 0, Log[2, mx]}, {j, 0, Log[6, mx]}, {k, 0, Log[30, mx]}, {m, 0, Log[210, mx]}]]], # <= mx &] (* Amiram Eldar, Apr 24 2020 after Robert G. Wilson v at A279537 *)

Prog

(Python)
from functools import lru_cache
from sympy import prime, integer_log
from oeis_sequences.OEISsequences import bisection
def A333964(n):
    @lru_cache(maxsize=None)
    def g(x, m, j): return sum(g(x//(prime(m)**i), m-1, i) for i in range(j, integer_log(x, prime(m))[0]+1)) if m-1 else max(0, x.bit_length()-j)
    def f(x): return n-1+x-sum(g(x, k, 1) for k in range(1, 5))
    return bisection(f, n, n) # Chai Wah Wu, Mar 27 2026
(Python)
from itertools import islice
from heapq import heappop, heappush
from sympy import factorint, prevprime, nextprime
def A333964_gen(): # generator of terms if the first n terms are desired.
    h, hset = [1], {1}
    while True:
        yield (m:=heappop(h))
        ps = factorint(m)
        for p in ps:
            if p == 2 or ps[prevprime(p)]>ps[p]:
                mp = m*p
                if mp not in hset:
                    heappush(h, mp)
                    hset.add(mp)
        if len(ps)<4:
            mp = m*nextprime(max(ps.keys(), default=1))
            if mp not in hset:
                heappush(h, mp)
                hset.add(mp)
A333964_list = list(islice(A333964_gen(), 40)) # Chai Wah Wu, Mar 27 2026

Crossrefs

Intersection of A025487 and A002473.

Cf. A025610, A279537.

Sequence in context: A362804 A095810 A025487 * A385722 A279537 A325238

Adjacent sequences: A333961 A333962 A333963 * A333965 A333966 A333967

Keyword

nonn

Author

David A. Corneth, Apr 20 2020

Status

approved