cp's OEIS Frontend

A225228 Numbers with prime signatures (1,1,1) or (2,2,1) or (3,2,2).

%I A225228 #6 Jul 28 2016 22:43:52
%S A225228 30,42,66,70,78,102,105,110,114,130,138,154,165,170,174,180,182,186,
%T A225228 190,195,222,230,231,238,246,252,255,258,266,273,282,285,286,290,300,
%U A225228 310,318,322,345,354,357,366,370,374,385,396,399,402,406,410,418,426,429
%N A225228 Numbers with prime signatures (1,1,1) or (2,2,1) or (3,2,2).
%C A225228 Union of A007304, A179643 and A179695; subsequence of A033992;
%C A225228 A001221(a(n)) = 3 and A051903(a(n)) <= A051904(a(n)) + 1 and A001222(a(n)) = 3 or 5 or 7;
%C A225228 A050326(a(n)) = 5.
%H A225228 Reinhard Zumkeller, <a href="/A225228/b225228.txt">Table of n, a(n) for n = 1..10000</a>
%F A225228 a(n) ~ 2n log n / (log log n)^2. - _Charles R Greathouse IV_, Jul 28 2016
%e A225228 A007304(1) = 2*3*5 = 30, A206778(30,1..8)=[1,2,3,5,6,10,15,30]:
%e A225228 A050326(30) = #{30, 15*2, 10*3, 6*5, 5*3*2} = 5;
%e A225228 A179643(1) = 2^2*3^2*5 = 180, A206778(180,1..8)=[1,2,3,5,6,10,15,30]:
%e A225228 A050326(180) = #{30*6, 30*3*2, 15*6*2, 10*6*3, 6*5*3*2} = 5;
%e A225228 A179695(1) = 2^3*3^2*5^2 = 1800, A206778(1800,1..8)=[1,2,3,5,6,10,15,30]:
%e A225228 A050326(1800) = #{30*10*6, 30*6*5*2, 30*10*3*2, 15*10*6*2, 10*6*5*3*2} = 5.
%o A225228 (Haskell)
%o A225228 a225228 n = a225228_list !! (n-1)
%o A225228 a225228_list = filter f [1..] where
%o A225228    f x = length es == 3 && sum es `elem` [3,5,7] &&
%o A225228                            maximum es - minimum es <= 1
%o A225228          where es = a124010_row x
%o A225228 (PARI) is(n)=my(f=vecsort(factor(n)[,2]~)); f==[1,1,1] || f==[1,2,2] || f==[2,2,3] \\ _Charles R Greathouse IV_, Jul 28 2016
%Y A225228 Cf. A124010.
%K A225228 nonn
%O A225228 1,1
%A A225228 _Reinhard Zumkeller_, May 03 2013