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 A269131 Composite numbers whose largest prime factor is less than its second-largest prime factor's square, counting with multiplicity so that the factors of 18 are 2, 3, 3. 1

%I

%S 4,6,8,9,12,15,16,18,21,24,25,27,30,32,35,36,42,45,48,49,50,54,55,60,

%T 63,64,65,70,72,75,77,81,84,85,90,91,95,96,98,100,105,108,110,115,119,

%U 120,121,125,126,128,130,133,135,140,143,144,147,150,154,161,162,165

%N Composite numbers whose largest prime factor is less than its second-largest prime factor's square, counting with multiplicity so that the factors of 18 are 2, 3, 3.

%C These are numbers that a naïve factoring algorithm can declare done at the penultimate prime factor.

%H Marc Moskowitz, <a href="/A269131/b269131.txt">Table of n, a(n) for n = 1..10000</a>

%t cnQ[n_]:=Module[{pfs=Flatten[Table[#[[1]],#[[2]]]&/@FactorInteger[n]]}, CompositeQ[ n]&&Last[pfs]<pfs[[-2]]^2]; Select[Range[200],cnQ] (* _Harvey P. Dale_, Nov 05 2017 *)

%o (PARI) is(n)=my(f=factor(n),e=#f~); e && (f[e,2]>1 || (e>1 && f[e-1,1]^2>f[e,1])) \\ _Charles R Greathouse IV_, Feb 19 2016

%o (Python)

%o seq = []

%o for n in range(2, 1000):

%o temp = n

%o factor = 2

%o while temp > 1:

%o if temp % factor == 0:

%o temp //= factor

%o if temp == 1:

%o continue

%o if temp < factor * factor:

%o seq.append(n)

%o else:

%o factor += 1

%o print(seq)

%K nonn,easy

%O 1,1

%A _Marc Moskowitz_, Feb 19 2016

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Last modified December 9 07:21 EST 2021. Contains 349627 sequences. (Running on oeis4.)