login
Table, row n is nonprime numbers k such that the largest divisor of n*k <= sqrt(n*k) is n.
4

%I #9 Jul 16 2015 21:56:35

%S 1,4,4,6,9,4,6,8,6,8,9,10,15,25,6,8,9,10,8,9,10,12,14,15,21,25,35,49,

%T 8,9,10,12,14,16,9,10,12,14,15,18,21,27,10,12,14,15,16,20,25,12,14,15,

%U 16,18,20,21,22,25,27,33,35,49,55,77,121,12,14,15,16,18,22,14,15,16,18,20

%N Table, row n is nonprime numbers k such that the largest divisor of n*k <= sqrt(n*k) is n.

%C Every prime > n also has this property.

%C If a*b is a composite number > n^2, with a <= b, then a*n and b are both > n, and one of them must be <= sqrt(n*a*b); thus n^2 is an upper bound for the numbers in row n.

%H Franklin T. Adams-Watters, <a href="/A163925/b163925.txt">Rows n=1..100 of table, flattened</a>

%e The table starts:

%e 1: 1

%e 2: 4

%e 3: 4,6,9

%e 4: 4,6,8

%e 5: 6,8,9,10,15,25

%e 6: 6,8,9,10

%o (PARI) arow(n)=local(v,d);v=[];for(k=n,n^2,if(!isprime(k),d=divisors(n*k);if(n==d[(#d+1)\2],v=concat(v,[k]))));v

%o (Haskell)

%o a163925 n k = a163925_tabf !! (n-1) !! (k-1)

%o a163925_tabf = map a163925_row [1..]

%o a163925_row n = [k | k <- takeWhile (<= n ^ 2) a018252_list,

%o let k' = k * n, let divs = a027750_row k',

%o last (takeWhile ((<= k') . (^ 2)) divs) == n]

%o -- _Reinhard Zumkeller_, Mar 15 2014

%Y Cf. A163926 (row lengths), A161344, A033676.

%Y Cf. A018252, A027750.

%K nonn,tabf,look

%O 1,2

%A _Franklin T. Adams-Watters_, Aug 06 2009