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A225228 Numbers with prime signatures (1,1,1) or (2,2,1) or (3,2,2). 6
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 (list; graph; refs; listen; history; text; internal format)
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 * A093599 A007304 A160350

Adjacent sequences:  A225225 A225226 A225227 * A225229 A225230 A225231

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, May 03 2013

STATUS

approved

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Last modified January 20 19:53 EST 2020. Contains 331096 sequences. (Running on oeis4.)