A163925 Table, row n is nonprime numbers k such that the largest divisor of n*k <= sqrt(n*k) is n.

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, 8, 9, 10, 12, 14, 16, 9, 10, 12, 14, 15, 18, 21, 27, 10, 12, 14, 15, 16, 20, 25, 12, 14, 15, 16, 18, 20, 21, 22, 25, 27, 33, 35, 49, 55, 77, 121, 12, 14, 15, 16, 18, 22, 14, 15, 16, 18, 20

Offset: 1

Author

Franklin T. Adams-Watters, Aug 06 2009

Keywords

• nonn
• tabf
• look

Comments

Every prime > n also has this property.

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.

Examples

			The table starts:
1: 1
2: 4
3: 4,6,9
4: 4,6,8
5: 6,8,9,10,15,25
6: 6,8,9,10
		

Links

• Franklin T. Adams-Watters, Rows n=1..100 of table, flattened

Crossrefs

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

Cf. A018252, A027750.

Programs

Haskell

a163925 n k = a163925_tabf !! (n-1) !! (k-1)
a163925_tabf = map a163925_row [1..]
a163925_row n = [k | k <- takeWhile (<= n ^ 2) a018252_list,
                     let k' = k * n, let divs = a027750_row k',
                     last (takeWhile ((<= k') . (^ 2)) divs) == n]
-- Reinhard Zumkeller, Mar 15 2014

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