A099992 Bisection of A025487.

1, 4, 8, 16, 30, 36, 60, 72, 120, 144, 192, 216, 256, 360, 420, 480, 576, 768, 864, 960, 1080, 1260, 1440, 1680, 1800, 2048, 2304, 2520, 2880, 3360, 3600, 4096, 4608, 5040, 5400, 6144, 6480, 6912, 7560, 7776, 8640, 9240, 10368, 11520, 12600, 13440, 13860

Offset

1,2

Comments

A025487: least integer of each prime signature; also products of primorial numbers A002110. - Robert G. Wilson v, Dec 14 2005

Links

Table of n, a(n) for n=1..47.

Mathematica

PrimeExponents[n_] := Last /@ FactorInteger@n; lpe = {}; ln = {1}; Do[ pe = Sort@PrimeExponents@n; If[FreeQ[lpe, pe], AppendTo[lpe, pe]; AppendTo[ln, n]], {n, 15000}]; ln[[2# - 1]] & /@ Range@(Length@ln/2) (* Robert G. Wilson v *)

Prog

(Python)
from itertools import count
from functools import lru_cache
from sympy import prime, integer_log
from oeis_sequences.OEISsequences import bisection
def A099992(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):
        c, p = (n-1<<1)+x, 1
        for k in count(1):
            p *= prime(k)
            if p>x:
                break
            c -= g(x, k, 1)
        return c
    return bisection(f, (n<<1)-1, (n<<1)-1) # Chai Wah Wu, Mar 26 2026

Crossrefs

Cf. A099993.

Sequence in context: A030119 A392391 A034451 * A301149 A301143 A215349

Adjacent sequences: A099989 A099990 A099991 * A099993 A099994 A099995

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 20 2004

Extensions

More terms from Robert G. Wilson v, Dec 14 2005

Status

approved