login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A077609 Triangle in which n-th row lists infinitary divisors of n. 23
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: A180184 A330752 A222266 * A077610 A329534 A317746

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 5 03:00 EDT 2021. Contains 346457 sequences. (Running on oeis4.)