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A027748 Triangle in which first row is 1, n-th row (n>1) lists distinct prime factors of n. 167
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(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)).

(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

{2}, {3}, {2}, {5}, {2, 3}, {7}, {2}, {3}, {2, 5}, {11}, ...

MAPLE

with(numtheory): [ seq(factorset(n), n=1..100) ];

MATHEMATICA

Flatten[ Table[ FactorInteger[n][[All, 1]], {n, 1, 62}]](* Jean-Fran├žois 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 xrange(2, 101):

....print [i for i in primefactors(n)] # Indranil Ghosh, Mar 31 2017

CROSSREFS

Cf. A000027, A001221, A001222, A027746, A141809, A141810.

a(A013939(A000040(n))+1) = A000040(n).

Cf. A020639, A027750.

Sequence in context: A129088 A086418 A100761 * A000705 A073751 A258581

Adjacent sequences:  A027745 A027746 A027747 * A027749 A027750 A027751

KEYWORD

nonn,easy,tabf,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Scott Lindhurst (ScottL(AT)alumni.princeton.edu)

STATUS

approved

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Last modified June 24 14:57 EDT 2017. Contains 288697 sequences.