A088723 Numbers k with at least one divisor d>1 such that d+1 also divides k.

6, 12, 18, 20, 24, 30, 36, 40, 42, 48, 54, 56, 60, 66, 72, 78, 80, 84, 90, 96, 100, 102, 108, 110, 112, 114, 120, 126, 132, 138, 140, 144, 150, 156, 160, 162, 168, 174, 180, 182, 186, 192, 198, 200, 204, 210, 216, 220, 222, 224, 228, 234, 240, 246, 252, 258, 260

Offset: 1

Author

Reinhard Zumkeller, Oct 12 2003

Keywords

• nonn

Comments

Complement of A088725.

Complement of A132895 relative to A005843, the even numbers. - Ray Chandler, May 29 2008

The numbers of terms that do not exceed 10^k, for k = 1, 2, ..., are 1, 21, 222, 2218, 22187, 221945, 2219452, 22194766, 221947862, 2219480686, ... . Apparently, the asymptotic density of this sequence exists and equals 0.22194... . - Amiram Eldar, Apr 20 2025

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A088722, A088724, A088725, A088726.

Cf. A027750, A008588 (subsequence).

Programs

Haskell

a088723 n = a088723_list !! (n-1)
a088723_list = filter f [2..] where
   f x = 1 `elem` (zipWith (-) (tail divs) divs)
         where divs = tail $ a027750_row x
-- Reinhard Zumkeller, Dec 16 2013

Mathematica

Select[Range[300],MemberQ[Differences[Select[Divisors[#], #>1&]], 1]&]  (* Harvey P. Dale, Apr 03 2011 *)

PARI

isok(k) = if(k%2, 0, if(!(k%3), 1, fordiv(k, d, if(d > 1 && !(k % (d+1)), return(1))); 0)); \\ Amiram Eldar, Apr 20 2025

Formula

A088722(a(n)) > 0.

Extensions

Extended by Ray Chandler, May 29 2008