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 A027748 Irregular triangle in which first row is 1, n-th row (n > 1) lists distinct prime factors of n. 188
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Number of terms in n-th row is A001221(n) for n > 1. From Reinhard Zumkeller, Aug 27 2011: (Start) A008472(n) = Sum_{k=1..A001221(n)} T(n,k), n>1; A007947(n) = Product_{k=1..A001221(n)} T(n,k); A006530(n) = Max_{k=1..A001221(n)} T(n,k). A020639(n) = Min_{k=1..A001221(n)} T(n,k). (End) Subsequence of A027750 that lists the divisors of n. - Michel Marcus, Oct 17 2015 LINKS T. D. Noe, Rows n=1..2048 of triangle, flattened Eric Weisstein's World of Mathematics, Distinct Prime Factors. EXAMPLE Triangle begins: 1; 2; 3; 2; 5; 2, 3; 7; 2; 3; 2, 5; 11; 2, 3; 13; 2, 7; ... MAPLE with(numtheory): [ seq(factorset(n), n=1..100) ]; MATHEMATICA Flatten[ Table[ FactorInteger[n][[All, 1]], {n, 1, 62}]](* Jean-François Alcover, Oct 10 2011 *) PROG (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 (Python) from sympy import primefactors for n in range(2, 101): print([i for i in primefactors(n)]) # Indranil Ghosh, Mar 31 2017 CROSSREFS Cf. A000027, A001221, A001222 (with repetition), A027746, A141809, A141810. a(A013939(A000040(n))+1) = A000040(n). Cf. A020639, A027750. A284411 gives column medians. Sequence in context: A086418 A100761 A336964 * A328852 A000705 A073751 Adjacent sequences: A027745 A027746 A027747 * A027749 A027750 A027751 KEYWORD nonn,easy,tabf,nice AUTHOR EXTENSIONS More terms from Scott Lindhurst (ScottL(AT)alumni.princeton.edu) STATUS approved

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Last modified December 1 23:44 EST 2022. Contains 358485 sequences. (Running on oeis4.)