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

1,1

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.

Links

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

Formula

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

Example

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.

Prog

(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

Crossrefs

Cf. A124010.

Sequence in context: A244066 A090815 A238367 * A336568 A350352 A093599

Adjacent sequences: A225225 A225226 A225227 * A225229 A225230 A225231

Keyword

nonn

Author

Reinhard Zumkeller, May 03 2013

Status

approved