A063718 - OEIS

%I #13 Jun 25 2018 22:57:36

%S 4,9,8,25,9,49,16,27,20,121,16,169,28,25,32,289,27,361,25,49,44,529,

%T 32,125,52,81,49,841,36,961,64,99,68,49,48,1369,76,117,50,1681,49,

%U 1849,88,75,92,2209,64,343,100,153,104,2809,81,121,64,171,116,3481,72,3721,124

%N a(n) is the smallest divisor of n^2 that is greater than n.

%C Larger of two distinct numbers with minimum sum whose geometric mean is n. E.g., a(12) = 16 as 12^2 = 144 = 1*144 = 2*72 = 3*48 = 4*36 = 6*24 = 8*18 = 9*16, etc. - _Amarnath Murthy_, Feb 15 2003

%H Harry J. Smith, <a href="/A063718/b063718.txt">Table of n, a(n) for n = 2..1000</a>

%e a(45)=75 because divisors of 45^2 are {1, 3, 5, 9, 15, 25, 27, 45, 75, 81, 135, 225, 405, 675, 2025} and the smallest element greater than 45 is 75.

%p with(numtheory): for n from 2 to 200 do a := divisors(n^2): b := a[(tau(n^2)-1)/2]: printf(`%d,`,n^2/b); od:

%t sdgn[n_]:=Select[Divisors[n^2],#>n&,1]; Flatten[Array[sdgn,70]] (* _Harvey P. Dale_, Jun 18 2012 *)

%o (PARI) { for (n=2, 1000, d=divisors(n^2); write("b063718.txt", n, " ", d[2 + length(d)\2]) ) } \\ _Harry J. Smith_, Aug 28 2009

%Y A063648(n) = n + a(n), A063717(n) = n^2/A063718(n), A063427(n) = n - a(n).

%Y Cf. A063717.

%K nonn

%O 2,1

%A _Vladeta Jovovic_, Aug 12 2001