login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 sizes of the distinct primes. Row 1 = (1). 18
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 (list; graph; refs; listen; history; text; internal format)
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. Adams-Watters, May 05 2011

A034684(n) = smallest term of n-th row; A028233(n) = T(n,1); A053585(n) = T(n,A001221(n)); A008475(n) = sum of n-th 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).

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 !! (k-1)

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

CROSSREFS

Cf. A141810, A027748.

Sequence in context: A161768 A213925 A141810 * A059711 A043265 A194459

Adjacent sequences:  A141806 A141807 A141808 * A141810 A141811 A141812

KEYWORD

nonn,tabf

AUTHOR

Leroy Quet, Jul 07 2008

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 13 09:05 EST 2017. Contains 295957 sequences.