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.

4, 6, 8, 9, 12, 15, 16, 18, 21, 24, 25, 27, 30, 32, 35, 36, 42, 45, 48, 49, 50, 54, 55, 60, 63, 64, 65, 70, 72, 75, 77, 81, 84, 85, 90, 91, 95, 96, 98, 100, 105, 108, 110, 115, 119, 120, 121, 125, 126, 128, 130, 133, 135, 140, 143, 144, 147, 150, 154, 161, 162, 165

Offset

1,1

Comments

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

Links

Marc Moskowitz, Table of n, a(n) for n = 1..10000

Mathematica

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 *)

Prog

(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
(Python)
seq = []
for n in range(2, 1000):
    temp = n
    factor = 2
    while temp > 1:
        if temp % factor == 0:
            temp //= factor
            if temp == 1:
                continue
            if temp < factor * factor:
                seq.append(n)
        else:
            factor += 1
print(seq)

Crossrefs

Sequence in context: A327446 A100425 A258614 * A130074 A304242 A067012

Adjacent sequences: A269128 A269129 A269130 * A269132 A269133 A269134

Keyword

nonn,easy

Author

Marc Moskowitz, Feb 19 2016

Status

approved