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A355467 a(n) is the smallest number which is greater than n and has more prime factors (with multiplicity) than n. 0
2, 4, 4, 8, 6, 8, 8, 16, 12, 12, 12, 16, 14, 16, 16, 32, 18, 24, 20, 24, 24, 24, 24, 32, 27, 27, 32, 32, 30, 32, 32, 64, 36, 36, 36, 48, 38, 40, 40, 48, 42, 48, 44, 48, 48, 48, 48, 64, 50, 54, 52, 54, 54, 64, 56, 64, 60, 60, 60, 64, 62, 63, 64, 128, 66, 72, 68, 72, 70, 72, 72, 96, 74, 75, 80, 80, 78, 80, 80, 96, 96 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Distinct from 2^A073093 because of the proviso that a(n) > n and bigomega(a(n)) > bigomega(n).

LINKS

Table of n, a(n) for n=1..81.

FORMULA

a(2^n) = 2^(n+1) because the smallest extra factor is 2.

a(3*2^n) = 2^(n+2) because 4 (i.e., 2^2) is the next biggest pair of factors.

EXAMPLE

For n = 1, a(1) = 2, since 2 is the first number satisfying 2 > 1 and bigomega(2) = 1 > bigomega(1) = 0.

For n = 5, a(5) = 8, since 8 is the first number satisfying 8 > 5 and bigomega(8) = 3 > bigomega(5) = 1.

For n = 12, a(12) = 16, since 16 is the first number satisfying 16 > 12 and bigomega(16) = 4 > bigomega(12) = 3.

PROG

(Haskell)

import Data.Numbers.Primes

result :: [Integer]

result = fmap (

  \n -> head (

      dropWhile (

          \m -> length (primeFactors m :: [Integer]) <= length (primeFactors n :: [Integer])

      )

      [n..]

  )

  ) [1..]

(PARI) a(n) = my(k=n+1, nb=bigomega(n)); while (bigomega(k) <= nb, k++); k; \\ Michel Marcus, Jul 05 2022

CROSSREFS

Cf. A073093, A001222.

Sequence in context: A005884 A229913 A285326 * A079890 A337973 A223592

Adjacent sequences:  A355464 A355465 A355466 * A355468 A355469 A355470

KEYWORD

nonn

AUTHOR

Dan Dart, Jul 03 2022

STATUS

approved

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Last modified August 18 12:29 EDT 2022. Contains 356212 sequences. (Running on oeis4.)