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

%I A088723 #22 Apr 20 2025 02:35:14
%S A088723 6,12,18,20,24,30,36,40,42,48,54,56,60,66,72,78,80,84,90,96,100,102,
%T A088723 108,110,112,114,120,126,132,138,140,144,150,156,160,162,168,174,180,
%U A088723 182,186,192,198,200,204,210,216,220,222,224,228,234,240,246,252,258,260
%N A088723 Numbers k with at least one divisor d>1 such that d+1 also divides k.
%C A088723 Complement of A088725.
%C A088723 Complement of A132895 relative to A005843, the even numbers. - _Ray Chandler_, May 29 2008
%C A088723 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
%H A088723 Reinhard Zumkeller, <a href="/A088723/b088723.txt">Table of n, a(n) for n = 1..10000</a>
%F A088723 A088722(a(n)) > 0.
%t A088723 Select[Range[300],MemberQ[Differences[Select[Divisors[#], #>1&]], 1]&]  (* _Harvey P. Dale_, Apr 03 2011 *)
%o A088723 (Haskell)
%o A088723 a088723 n = a088723_list !! (n-1)
%o A088723 a088723_list = filter f [2..] where
%o A088723    f x = 1 `elem` (zipWith (-) (tail divs) divs)
%o A088723          where divs = tail $ a027750_row x
%o A088723 -- _Reinhard Zumkeller_, Dec 16 2013
%o A088723 (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
%Y A088723 Cf. A088722, A088724, A088725, A088726.
%Y A088723 Cf. A027750, A008588 (subsequence).
%K A088723 nonn
%O A088723 1,1
%A A088723 _Reinhard Zumkeller_, Oct 12 2003
%E A088723 Extended by _Ray Chandler_, May 29 2008