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A355467
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a(n) is the smallest number which is greater than n and has more prime factors (with multiplicity) than n.
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0
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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
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OFFSET
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1,1
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COMMENTS
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Distinct from 2^A073093 because of the proviso that a(n) > n and bigomega(a(n)) > bigomega(n).
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LINKS
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Table of n, a(n) for n=1..81.
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FORMULA
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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.
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EXAMPLE
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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.
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PROG
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(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
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CROSSREFS
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Cf. A073093, A001222.
Sequence in context: A005884 A229913 A285326 * A079890 A337973 A223592
Adjacent sequences: A355464 A355465 A355466 * A355468 A355469 A355470
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KEYWORD
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nonn
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AUTHOR
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Dan Dart, Jul 03 2022
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STATUS
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approved
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