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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A077609 Triangle in which n-th row lists infinitary divisors of n. 7
1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 2, 3, 6, 1, 7, 1, 2, 4, 8, 1, 9, 1, 2, 5, 10, 1, 11, 1, 3, 4, 12, 1, 13, 1, 2, 7, 14, 1, 3, 5, 15, 1, 16, 1, 17, 1, 2, 9, 18, 1, 19, 1, 4, 5, 20, 1, 3, 7, 21, 1, 2, 11, 22, 1, 23, 1, 2, 3, 4, 6, 8, 12, 24, 1, 25, 1, 2, 13, 26, 1, 3, 9, 27, 1, 4, 7, 28, 1, 29, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Reinhard Zumkeller, Rows n = 1..1000 of table, flattened

G. L. Cohen, P. Hagis, Jr, Arithmetic functions associated with the infinitary divisors of an integer, Internat. J. Math. Math. Sci. 16 (2) (1993) 373-384

Eric Weisstein's World of Mathematics, Infinitary Divisor

EXAMPLE

The first few rows are:

1;

1, 2;

1, 3;

1, 4;

1, 5;

1, 2, 3, 6;

1, 7;

1, 2, 4, 8;

1, 9;

1, 2, 5, 10;

1, 11;

1, 3, 4, 12;

MAPLE

# see the function idivisors() in A049417. # R. J. Mathar, Oct 05 2017

MATHEMATICA

f[x_] := If[x == 1, 1, Sort@ Flatten@ Outer[Times, Sequence @@ (FactorInteger[x] /. {p_, m_Integer} :> p^Select[Range[0, m], BitOr[m, #] == m &])]] ; Array[f, 30] // Flatten (* Paul Abbott (paul(AT)physics.uwa.edu.au), Apr 29 2005 *) (* edited by Michael De Vlieger, Jun 07 2016 *)

PROG

(Haskell)

import Data.List ((\\))

a077609 n k = a077609_row n !! (k-1)

a077609_row n = filter

   (\d -> d == 1 || null (a213925_row d \\ a213925_row n)) $ a027750_row n

a077609_tabf = map a077609_row [1..]

-- Reinhard Zumkeller, Jul 10 2013

(PARI) isidiv(d, f) = {if (d==1, return (1)); for (k=1, #f~, bne = binary(f[k, 2]); bde = binary(valuation(d, f[k, 1])); if (#bde < #bne, bde = concat(vector(#bne-#bde), bde)); for (j=1, #bne, if (! bne[j] && bde[j], return (0)); ); ); return (1); }

row(n) = {d = divisors(n); f = factor(n); idiv = []; for (k=1, #d, if (isidiv(d[k], f), idiv = concat(idiv, d[k])); ); idiv; } \\ Michel Marcus, Feb 15 2016

CROSSREFS

Cf. A027750, A037445, A049417 (row sums).

Sequence in context: A049077 A180184 A222266 * A077610 A228179 A319338

Adjacent sequences:  A077606 A077607 A077608 * A077610 A077611 A077612

KEYWORD

nonn,tabf

AUTHOR

Eric W. Weisstein, Nov 11 2002

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 November 18 01:00 EST 2018. Contains 317279 sequences. (Running on oeis4.)