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A027748 Irregular triangle in which first row is 1, n-th row (n > 1) lists distinct prime factors of n. 226
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
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).
A284411 gives column medians.
Sequence in context: A086418 A100761 A336964 * A361650 A328852 A000705
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 March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)