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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
OFFSET
1,1
LINKS
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
KEYWORD
nonn
AUTHOR
Hieronymus Fischer, Oct 23 2007
EXTENSIONS
Sequence definition corrected and examples added by Hieronymus Fischer, Apr 05 2013
STATUS
approved