|
| |
|
|
A027748
|
|
Irregular triangle in which first row is 1, n-th row (n > 1) lists distinct prime factors of n.
|
|
193
|
|
|
|
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
|
N. J. A. Sloane
|
|
|
EXTENSIONS
|
More terms from Scott Lindhurst (ScottL(AT)alumni.princeton.edu)
|
|
|
STATUS
|
approved
|
| |
|
|
