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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 (list; graph; refs; listen; history; text; internal format)
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
CROSSREFS
Sequence in context: A181794 A199536 A284883 * A114331 A102070 A026402
KEYWORD
nonn
AUTHOR
Hieronymus Fischer, Oct 23 2007
EXTENSIONS
Sequence definition corrected and examples added by Hieronymus Fischer, Apr 05 2013
STATUS
approved

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Last modified July 17 09:24 EDT 2024. Contains 374363 sequences. (Running on oeis4.)