

A163925


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


4



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
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OFFSET

1,2


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.


LINKS

Franklin T. AdamsWatters, Rows n=1..100 of table, flattened


EXAMPLE

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


PROG

(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
(Haskell)
a163925 n k = a163925_tabf !! (n1) !! (k1)
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


CROSSREFS

Cf. A163926 (row lengths), A161344, A033676.
Cf. A018252, A027750.
Sequence in context: A222732 A074161 A201401 * A200609 A128037 A102414
Adjacent sequences: A163922 A163923 A163924 * A163926 A163927 A163928


KEYWORD

nonn,tabf,look


AUTHOR

Franklin T. AdamsWatters, Aug 06 2009


STATUS

approved



