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A056608
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Least prime factor of the n-th composite number.
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39
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2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 5, 2, 3, 2, 2, 2, 3, 2, 5, 2, 2, 3, 2, 2, 2, 3, 2, 2, 7, 2, 3, 2, 2, 5, 2, 3, 2, 2, 2, 3, 2, 5, 2, 2, 3, 2, 2, 2, 3, 2, 7, 2, 2, 3, 2, 2, 5, 2, 3, 2, 2, 7, 2, 3, 2, 5, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 5, 2, 3, 2, 7, 2, 11, 2, 3, 2, 5, 2, 2, 3, 2, 2, 7, 2, 3, 2, 2, 2
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OFFSET
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1,1
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COMMENTS
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Record values are seen when n = A120389(m). Conjecture: at each new record the count of the prior record follows A247509. Records seen are 2, 3, 5, 7, 11, ... and when 3, 5, 7, 11 are first seen, there have been 3, 3, 2, and 4 occurrences of 2, 3, 5, and 7. These are A247509(1) through A247509(4). Thus, the count for prime(60) would be A247509(60). - Bill McEachen, Jun 17 2024
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LINKS
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FORMULA
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MATHEMATICA
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DeleteCases[Table[FactorInteger[n][[1, 1]] * Boole[Not[PrimeQ[n]]], {n, 2, 100}], 0] (* Alonso del Arte, Aug 21 2014 *)
FactorInteger[#][[1, 1]]&/@Select[Range[200], CompositeQ] (* Harvey P. Dale, Mar 16 2023 *)
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PROG
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(Magma) [ PrimeDivisors(n)[1]: n in [2..140] | not IsPrime(n) ]; // Klaus Brockhaus, Jun 23 2009
(Haskell)
(PARI) forcomposite(n=1, 1e2, p=factor(n)[1, 1]; print1(p, ", ")) \\ Felix Fröhlich, Aug 03 2014
(Python)
from sympy import composite, factorint
return min(factorint(composite(n))) # Chai Wah Wu, Jul 22 2019
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CROSSREFS
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Cf. A052369 (largest prime factor of n, where n runs through composite numbers). - Klaus Brockhaus, Jun 23 2009
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KEYWORD
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easy,nonn,changed
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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