A178212 Nonsquarefree numbers divisible by exactly three distinct primes.

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

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 !! (n-1)
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: A349758 A217740 A123712 * A182855 A350371 A009129

Adjacent sequences: A178209 A178210 A178211 * A178213 A178214 A178215

Keyword

nonn

Author

Reinhard Zumkeller, May 24 2010

Status

approved