

A141809


Irregular table: Row n (of A001221(n) terms, for n>=2) consists of the largest powers that divides n of each distinct prime that divides n. Terms are arranged by the size of the distinct primes. Row 1 = (1).


21



1, 2, 3, 4, 5, 2, 3, 7, 8, 9, 2, 5, 11, 4, 3, 13, 2, 7, 3, 5, 16, 17, 2, 9, 19, 4, 5, 3, 7, 2, 11, 23, 8, 3, 25, 2, 13, 27, 4, 7, 29, 2, 3, 5, 31, 32, 3, 11, 2, 17, 5, 7, 4, 9, 37, 2, 19, 3, 13, 8, 5, 41, 2, 3, 7, 43, 4, 11, 9, 5, 2, 23, 47, 16, 3, 49, 2, 25, 3, 17, 4, 13, 53, 2, 27, 5, 11, 8, 7, 3
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OFFSET

1,2


COMMENTS

In other words, except for row 1, row n contains the unitary prime power divisors of n, sorted by the prime.  Franklin T. AdamsWatters, May 05 2011
A034684(n) = smallest term of nth row; A028233(n) = T(n,1); A053585(n) = T(n,A001221(n)); A008475(n) = sum of nth row for n > 1.  Reinhard Zumkeller, Jan 29 2013


LINKS

Reinhard Zumkeller, Rows n=1..10000 of triangle, flattened
Eric Weisstein's World of Mathematics, Prime Factorization


FORMULA

T(n,k) = A027748(n,k)^A124010(n,k) for n > 1, k = 1 .. A001221(n).  Reinhard Zumkeller, Mar 15 2012


EXAMPLE

60 has the prime factorization 2^2 * 3^1 * 5^1, so row 60 is (4,3,5).
From M. F. Hasler, Oct 12 2018: (Start)
The table starts:
n : largest prime powers dividing n
1 : 1
2 : 2
3 : 3
4 : 4
5 : 5
6 : 2, 3
7 : 7
8 : 8
9 : 9
10 : 2, 5
11 : 11
12 : 4, 3
etc. (End)


MATHEMATICA

f[{x_, y_}] := x^y; Table[Map[f, FactorInteger[n]], {n, 1, 50}] // Grid (* Geoffrey Critzer, Apr 03 2015 *)


PROG

(Haskell)
a141809 n k = a141809_row n !! (k1)
a141809_row 1 = [1]
a141809_row n = zipWith (^) (a027748_row n) (a124010_row n)
a141809_tabf = map a141809_row [1..]
 Reinhard Zumkeller, Mar 18 2012
(PARI) A141809_row(n)=if(n>1, apply(factorback, Col(factor(n)))~, [1]) \\ M. F. Hasler, Oct 12 2018


CROSSREFS

A027748, A124010 are used in a formula defining this sequence.
Cf. A001221 (row lengths), A008475 (row sums), A028233 (column 1), A034684 (row minima), A053585 (right edge).
Cf. A060175, A141810, A213925.
Sequence in context: A161768 A213925 A141810 * A309435 A043265 A194459
Adjacent sequences: A141806 A141807 A141808 * A141810 A141811 A141812


KEYWORD

nonn,tabf


AUTHOR

Leroy Quet, Jul 07 2008


STATUS

approved



