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!)
A027750 Triangle read by rows in which row n lists the divisors of n. 313
1, 1, 2, 1, 3, 1, 2, 4, 1, 5, 1, 2, 3, 6, 1, 7, 1, 2, 4, 8, 1, 3, 9, 1, 2, 5, 10, 1, 11, 1, 2, 3, 4, 6, 12, 1, 13, 1, 2, 7, 14, 1, 3, 5, 15, 1, 2, 4, 8, 16, 1, 17, 1, 2, 3, 6, 9, 18, 1, 19, 1, 2, 4, 5, 10, 20, 1, 3, 7, 21, 1, 2, 11, 22, 1, 23, 1, 2, 3, 4, 6, 8, 12, 24, 1, 5, 25, 1, 2, 13, 26, 1, 3, 9, 27, 1, 2, 4, 7, 14, 28, 1, 29 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Or, in the list of natural numbers (A000027), replace n with its divisors.

This gives the first elements of the ordered pairs (a,b) a >= 1, b >= 1 ordered by their product ab.

Also, row n lists the largest parts of the partitions of n whose parts are not distinct. - Omar E. Pol, Sep 17 2008

Concatenation of n-th row gives A037278(n). - Reinhard Zumkeller, Aug 07 2011

{A210208(n,k): k=1..A073093(n)} subset of {T(n,k): k=1..A000005(n)} for all n. - Reinhard Zumkeller, Mar 18 2012

Row sums give A000203. Right border gives A000027. - Omar E. Pol, Jul 29 2012

Indices of records are in A006218. - Irina Gerasimova, Feb 27 2013

The number of primes in the n-th row is omega(n) = A001221(n). - Michel Marcus, Oct 21 2015

The row polynomials P(n,x) = Sum_{k=1..A000005(n)} T(n,k)*x^k with composite n which are irreducible over the integers are given in A292226. - Wolfdieter Lang, Nov 09 2017

LINKS

Franklin T. Adams-Watters, Rows 1..1000, flattened

Franklin T. Adams-Watters, Rows 1..10000

Omar E. Pol, Illustration of initial terms - Omar E. Pol, Oct 22 2009

Eric Weisstein's World of Mathematics, Divisor

Wikipedia, Table of divisors

Index entries for sequences related to divisors of numbers

FORMULA

a(A006218(n-1) + k) = k-divisor of n, 1 <= k <= A000005(n). - Reinhard Zumkeller, May 10 2006

T(n,k) = n / A056538(n,k) = A056538(n,n-k+1), 1 <= k <= A000005(n). - Reinhard Zumkeller, Sep 28 2014

EXAMPLE

Triangle begins:

1;

1, 2;

1, 3;

1, 2, 4;

1, 5;

1, 2, 3, 6;

1, 7;

1, 2, 4, 8;

1, 3, 9;

1, 2, 5, 10;

1, 11;

1, 2, 3, 4, 6, 12;

MAPLE

seq(op(numtheory:-divisors(a)), a = 1 .. 20) # Matt C. Anderson, May 15 2017

MATHEMATICA

Flatten[ Table[ Flatten [ Divisors[ n ] ], {n, 1, 30} ] ]

PROG

(MAGMA) [Divisors(n) : n in [1..20]];

(Haskell)

a027750 n k = a027750_row n !! (k-1)

a027750_row n = filter ((== 0) . (mod n)) [1..n]

a027750_tabf = map a027750_row [1..]

-- Reinhard Zumkeller, Jan 15 2011, Oct 21 2010

(PARI) v=List(); for(n=1, 20, fordiv(n, d, listput(v, d))); Vec(v) \\ Charles R Greathouse IV, Apr 28 2011

(Python)

from sympy import divisors

for n in xrange(1, 16):

....print [i for i in divisors(n)] # Indranil Ghosh, Mar 30 2017

CROSSREFS

Cf. A000005 (row length), A001221, A027749, A027751, A056534, A056538, A127093, A135010, A161700, A163280, A240698 (partial sums of rows), A240694 (partial products of rows), A247795 (parities). A292226.

Sequence in context: A210208 A162306 A233773 * A275055 A254679 A275280

Adjacent sequences:  A027747 A027748 A027749 * A027751 A027752 A027753

KEYWORD

nonn,easy,tabf,look

AUTHOR

N. J. A. Sloane

EXTENSIONS

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

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 12 01:08 EST 2017. Contains 295936 sequences.