

A269131


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


1



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
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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[e1, 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



