cp's OEIS Frontend

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

%I A163925 #9 Jul 16 2015 21:56:35
%S A163925 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 A163925 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 A163925 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 A163925 Table, row n is nonprime numbers k such that the largest divisor of n*k <= sqrt(n*k) is n.
%C A163925 Every prime > n also has this property.
%C A163925 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 A163925 Franklin T. Adams-Watters, <a href="/A163925/b163925.txt">Rows n=1..100 of table, flattened</a>
%e A163925 The table starts:
%e A163925 1: 1
%e A163925 2: 4
%e A163925 3: 4,6,9
%e A163925 4: 4,6,8
%e A163925 5: 6,8,9,10,15,25
%e A163925 6: 6,8,9,10
%o A163925 (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 A163925 (Haskell)
%o A163925 a163925 n k = a163925_tabf !! (n-1) !! (k-1)
%o A163925 a163925_tabf = map a163925_row [1..]
%o A163925 a163925_row n = [k | k <- takeWhile (<= n ^ 2) a018252_list,
%o A163925                      let k' = k * n, let divs = a027750_row k',
%o A163925                      last (takeWhile ((<= k') . (^ 2)) divs) == n]
%o A163925 -- _Reinhard Zumkeller_, Mar 15 2014
%Y A163925 Cf. A163926 (row lengths), A161344, A033676.
%Y A163925 Cf. A018252, A027750.
%K A163925 nonn,tabf,look
%O A163925 1,2
%A A163925 _Franklin T. Adams-Watters_, Aug 06 2009