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A027748
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Triangle in which first row is 1, n-th row (n>1) lists distinct prime factors of n.
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94
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1, 2, 3, 2, 5, 2, 3, 7, 2, 3, 2, 5, 11, 2, 3, 13, 2, 7, 3, 5, 2, 17, 2, 3, 19, 2, 5, 3, 7, 2, 11, 23, 2, 3, 5, 2, 13, 3, 2, 7, 29, 2, 3, 5, 31, 2, 3, 11, 2, 17, 5, 7, 2, 3, 37, 2, 19, 3, 13, 2, 5, 41, 2, 3, 7, 43, 2, 11, 3, 5, 2, 23, 47, 2, 3, 7, 2, 5, 3, 17, 2, 13, 53, 2, 3, 5, 11, 2, 7, 3, 19, 2, 29, 59, 2, 3, 5, 61, 2, 31
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OFFSET
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1,2
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COMMENTS
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Number of terms in n-th row is A001221(n) for n>1.
A008472(n)=Sum(T(n,k):1<=k<=A001221(n)), n>1; A007947(n)=Product(T(n,k):1<=k<=A001221(n)); A006530(n)=Max(T(n,k):1<=k<=A001221(n)); A020639(n)=Min(T(n,k):1<=k<=A001221(n)). [Reinhard Zumkeller, Aug 27 2011]
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LINKS
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T. D. Noe, Rows n=1..2048 of triangle, flattened
Eric Weisstein's World of Mathematics, Distinct Prime Factors.
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EXAMPLE
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{2}, {3}, {2}, {5}, {2, 3}, {7}, {2}, {3}, {2, 5}, {11},...
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MAPLE
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with(numtheory): [ seq(factorset(n), n=1..100) ];
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MATHEMATICA
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Flatten[ Table[ FactorInteger[n][[All, 1]], {n, 1, 62}]](* From Jean-François Alcover, Oct 10 2011 *)
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PROG
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(Haskell)
import Data.List (unfoldr)
a027748 n k = a027748_tabl !! (n-1) !! (k-1)
a027748_tabl = map a027748_row [1..]
a027748_row 1 = [1]
a027748_row n = unfoldr fact n where
fact 1 = Nothing
fact x = Just (p, until ((> 0) . (`mod` p)) (`div` p) x)
where p = a020639 x -- smallest prime factor of x
-- Reinhard Zumkeller, Aug 27 2011
(PARI) print1(1); for(n=2, 20, f=factor(n)[, 1]; for(i=1, #f, print1(", "f[i]))) \\ Charles R Greathouse IV, Mar 20 2013
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CROSSREFS
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Cf. A000027, A001221, A001222, A027746, A141809, A141810.
a(A013939(A000040(n))+1) = A000040(n).
Cf. A020639.
Sequence in context: A129088 A086418 A100761 * A000705 A073751 A108501
Adjacent sequences: A027745 A027746 A027747 * A027749 A027750 A027751
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KEYWORD
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nonn,easy,tabf,nice
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Scott Lindhurst (ScottL(AT)alumni.princeton.edu)
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STATUS
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approved
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