A085154 a(n+1) = smallest number >a(n) having more prime factors than a(n), with or without repetitions; a(1)=1.

1, 2, 4, 6, 8, 10, 12, 16, 18, 24, 30, 32, 33, 36, 42, 48, 60, 64, 65, 66, 72, 78, 80, 84, 96, 102, 104, 105, 108, 110, 112, 114, 120, 128, 129, 130, 132, 144, 150, 160, 165, 168, 192, 195, 196, 198, 200, 204, 208, 210, 216, 220, 224, 228, 240, 256, 258, 260

Offset

1,2

Comments

A001221(a(n+1))>A001221(a(n)) or A001222(a(n+1))>A001222(a(n)).

Links

Table of n, a(n) for n=1..58.

Mathematica

a[n_] := a[n] = If[n == 1, 1, Module[{k, nu, om}, For[k = a[n-1]+1; nu = PrimeNu[a[n-1]]; om = PrimeOmega[a[n-1]], True, k++, If[PrimeNu[k] > nu || PrimeOmega[k] > om, Return[k]]]]];
Array[a, 100] (* Jean-François Alcover, Oct 07 2021 *)

Prog

(Python)
from sympy import factorint
def aupton(terms):
    alst, wn, Wn, k = [1], 0, 0, 1
    while len(alst) < terms:
        while True:
            k += 1
            pf = factorint(k, multiple=True)
            wk, Wk = len(pf), len(set(pf))
            if wk > wn or Wk > Wn:
                break
        alst.append(k)
        wn, Wn = wk, Wk
    return alst
print(aupton(58)) # Michael S. Branicky, Oct 07 2021

Crossrefs

Cf. A001221, A001222.

Sequence in context: A114270 A109884 A015926 * A371286 A331079 A274284

Adjacent sequences: A085151 A085152 A085153 * A085155 A085156 A085157

Keyword

nonn

Author

Reinhard Zumkeller, Aug 10 2003

Status

approved