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

30, 42, 66, 70, 78, 102, 105, 110, 114, 130, 138, 154, 165, 170, 174, 180, 182, 186, 190, 195, 222, 230, 231, 238, 246, 252, 255, 258, 266, 273, 282, 285, 286, 290, 300, 310, 318, 322, 345, 354, 357, 366, 370, 374, 385, 396, 399, 402, 406, 410, 418, 426, 429

Offset: 1

Author

Reinhard Zumkeller, May 03 2013

Keywords

• nonn

Comments

Union of A007304, A179643 and A179695; subsequence of A033992;

A001221(a(n)) = 3 and A051903(a(n)) <= A051904(a(n)) + 1 and A001222(a(n)) = 3 or 5 or 7;

A050326(a(n)) = 5.

Examples

			A007304(1) = 2*3*5 = 30, A206778(30,1..8)=[1,2,3,5,6,10,15,30]:
A050326(30) = #{30, 15*2, 10*3, 6*5, 5*3*2} = 5;
A179643(1) = 2^2*3^2*5 = 180, A206778(180,1..8)=[1,2,3,5,6,10,15,30]:
A050326(180) = #{30*6, 30*3*2, 15*6*2, 10*6*3, 6*5*3*2} = 5;
A179695(1) = 2^3*3^2*5^2 = 1800, A206778(1800,1..8)=[1,2,3,5,6,10,15,30]:
A050326(1800) = #{30*10*6, 30*6*5*2, 30*10*3*2, 15*10*6*2, 10*6*5*3*2} = 5.
		

Links

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

Crossrefs

Cf. A124010.

Programs

Haskell

a225228 n = a225228_list !! (n-1)
a225228_list = filter f [1..] where
   f x = length es == 3 && sum es `elem` [3,5,7] &&
                           maximum es - minimum es <= 1
         where es = a124010_row x

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

Formula

a(n) ~ 2n log n / (log log n)^2. - Charles R Greathouse IV, Jul 28 2016