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

Author

Marc Moskowitz, Feb 19 2016

Keywords

• nonn
• easy

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

Crossrefs

Cf. A002808, A251728 (semiprime terms).

Subsequence of A253567.

Programs

Mathematica

cnQ[n_]:=Module[{pfs=Flatten[Table[#[[1]],#[[2]]]&/@FactorInteger[n]]}, CompositeQ[ n]&&Last[pfs]Harvey P. Dale, Nov 05 2017 *)

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)