

A134333


Numbers n whose number of prime factors (counted with multiplicity) is a prime factor of n.


28



4, 6, 10, 12, 14, 18, 22, 26, 27, 30, 34, 38, 42, 45, 46, 58, 62, 63, 66, 74, 75, 78, 80, 82, 86, 94, 99, 102, 105, 106, 114, 117, 118, 120, 122, 134, 138, 142, 146, 147, 153, 158, 165, 166, 171, 174, 178, 180, 186, 194, 195, 200, 202, 206, 207, 214, 218, 222, 226
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OFFSET

1,1


LINKS

Hieronymus Fischer, Table of n, a(n) for n = 1..10000


FORMULA

a(n) << n log n/(log log n)^k for any fixed k.  Charles R Greathouse IV, Sep 14 2015


EXAMPLE

a(1) = 4, since 4 has 2 prime factors and 2 is a prime factor of 4.
a(4) = 12, since 12 = 2*2*3 has 3 prime factors, and 3 is a prime factor of 12.
a(21) = 75, since 75 = 3*3*5 has 3 prime factors. and 3 is a prime factor of 75.
9 = 3*3 is not a term, since the number of prime factors (=2) is not a divisor of 9.
28 = 2*2*7 is not a term, since the number of prime factors (=3) is not a divisor of 28.


MATHEMATICA

fQ[n_] := Module[{d = Total[Transpose[FactorInteger[n]][[2]]]}, PrimeQ[d] && Mod[n, d] == 0]; Select[Range[2, 226], fQ] (* T. D. Noe, Apr 05 2013 *)


PROG

(PARI) a(n)=my(t=bigomega(n)); n%t==0 && isprime(t) \\ Charles R Greathouse IV, Sep 14 2015


CROSSREFS

Cf. A000040, A001222, A100118, A046363, A133620, A133621, A133880, A133890, A133900, A133910, A133911, A134330, A134331, A134332, A134334, A134344, A134376, A063989.
Sequence in context: A181794 A199536 A284883 * A114331 A102070 A026402
Adjacent sequences: A134330 A134331 A134332 * A134334 A134335 A134336


KEYWORD

nonn


AUTHOR

Hieronymus Fischer, Oct 23 2007


EXTENSIONS

Sequence definition corrected and examples added by Hieronymus Fischer, Apr 05 2013


STATUS

approved



