A134333 Numbers n whose number of prime factors (counted with multiplicity) is a prime factor of n.

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

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, A046346, 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