

A195086


Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 2.


14



8, 24, 27, 36, 40, 54, 56, 88, 100, 104, 120, 125, 135, 136, 152, 168, 180, 184, 189, 196, 225, 232, 248, 250, 252, 264, 270, 280, 296, 297, 300, 312, 328, 343, 344, 351, 375, 376, 378, 396, 408, 424, 440, 441, 450, 456, 459, 468, 472, 484, 488
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OFFSET

1,1


COMMENTS

Numbers whose powerful part (A057521) is either a cube of a prime (A030078) or a square of a squarefree semiprime (A085986).
The asymptotic density of this sequence is (6/Pi^2) * (Sum_{p prime} 1/(p^2*(p+1)) + Sum_{p<q primes} 1/(p*(p+1)*q*(q+1))) = (1/zeta(2)) * (2*P(3) + Sum_{k>=4} (1)^(k+1)*(k1)*P(k) + (Sum_{k>=2} (1)^k*P(k))^2))/2 = 0.0963023158..., where P is the prime zeta function. (End)


LINKS



FORMULA



MATHEMATICA

Select[Range[500], PrimeOmega[#]PrimeNu[#]==2&]


PROG

(Haskell)
a195086 n = a195086_list !! (n1)
a195086_list = filter ((== 2) . a046660) [1..]


CROSSREFS

Cf. A001221, A001222, A025487, A057521, A060687, A195069, A195087, A195088, A195089, A195090, A195091, A195092, A195093, A046660, A257851, A261256, A264959.


KEYWORD

nonn,changed


AUTHOR



STATUS

approved



