

A178212


Nonsquarefree numbers divisible by exactly three distinct primes.


6



60, 84, 90, 120, 126, 132, 140, 150, 156, 168, 180, 198, 204, 220, 228, 234, 240, 252, 260, 264, 270, 276, 280, 294, 300, 306, 308, 312, 315, 336, 340, 342, 348, 350, 360, 364, 372, 378, 380, 396, 408, 414, 440, 444, 450, 456, 460, 468, 476, 480, 490, 492
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OFFSET

1,1


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000


FORMULA

A001221(a(n)) = 3; A001222(a(n)) > 3; A000005(n) >= 12;
a(n) = A123712(n) for n <= 52, possibly more.


EXAMPLE

60 is in the sequence because it is not squarefree and it is divisible by three distinct primes: 2, 3, 5.
72 is not in the sequence, because although it is not squarefree, it is divisible by only two distinct primes: 2 and 3.


MATHEMATICA

nsD3Q[n_] := Block[{fi = FactorInteger@ n}, Length@ fi == 3 && Plus @@ Last /@ fi > 3]; Select[ Range@ 494, nsD3Q] (* Robert G. Wilson v, Feb 09 2012 *)
Select[Range[500], PrimeNu[#] == 3 && PrimeOmega[#] > 3 &] (* Alonso del Arte, Mar 23 2015, based on a comment from Robert G. Wilson v, Feb 09 2012; requires Mathematica 7.0+ *)


PROG

(PARI) is_A178212(n)={ omega(n)==3 & bigomega(n)>3 }
for(n=1, 999, is_A178212(n) & print1(n", ")) \\ M. F. Hasler, Feb 09 2012
(Haskell)
a178212 n = a178212_list !! (n1)
a178212_list = filter f [1..] where
f x = length (a027748_row x) == 3 && any (> 1) (a124010_row x)
 Reinhard Zumkeller, Apr 03 2015


CROSSREFS

A subsequence of A033987.
A085987 is a subsequence.
Cf. A007304, A200511, A200521.
Cf. A000005, A001221, A001222, A013929, A085987, A123712.
Cf. A027748, A124010.
Sequence in context: A261375 A217740 A123712 * A182855 A009129 A174292
Adjacent sequences: A178209 A178210 A178211 * A178213 A178214 A178215


KEYWORD

nonn


AUTHOR

Reinhard Zumkeller, May 24 2010


STATUS

approved



