

A342090


Numbers with at least one prime power p^e in their prime factorization such that pe.


8



4, 12, 16, 20, 27, 28, 36, 44, 48, 52, 54, 60, 64, 68, 76, 80, 84, 92, 100, 108, 112, 116, 124, 132, 135, 140, 144, 148, 156, 164, 172, 176, 180, 188, 189, 192, 196, 204, 208, 212, 216, 220, 228, 236, 240, 244, 252, 256, 260, 268, 270, 272, 276, 284, 292, 297, 300
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OFFSET

1,1


COMMENTS

Numbers with a unitary divisor of the form p^(m*p) where p is a prime and m > 0.
The numbers of terms that do not exceed 10^k, for k = 1, 2, ..., are 1, 19, 188, 1883, 18825, 188244, 1882429, 18824297, 188242957, 1882429628, ...
The asymptotic density of this sequence is 1  Product_{p prime} 1  (p  1)/(p*(p^p  1)) = 0.18824296270011399086...


LINKS



EXAMPLE

4 = 2^2 is a term since 2 divides 2.
8 = 2^3 is not a term since 2 does not divide 3.


MATHEMATICA

q[n_] := AnyTrue[FactorInteger[n], Divisible[Last[#], First[#]] &]; Select[Range[2, 300], q]


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



