login
Smallest number with n unrelated numbers (numbers which are neither coprime nor a divisor), or 0 if no such number exists.
3

%I #4 Dec 05 2013 19:55:19

%S 3,6,0,10,15,14,21,18,35,22,33,26,39,0,65,30,36,38,57,44,95,46,63,42,

%T 115,50,64,58,87,54,75,68,155,60,99,74,111,72,185,66,117,86,129,92,

%U 215,94,141,78,235,84,105,98,100,96,265,90,135,118,147,122,183,108

%N Smallest number with n unrelated numbers (numbers which are neither coprime nor a divisor), or 0 if no such number exists.

%C The 0's are only conjectures (search extended to 2000).

%e a(0) = 4, as 4 has no unrelated numbers less than it. a(5) = 14. The unrelated numbers pertaining to 14 are 4,6,8 10 and 12.

%o (PARI) for(n=0,100,s=-1:k=2:while(s!=n&&k<2000,k=k+1:s=0:for(l=2,k-1,if((k%l>0)&&gcd(k,l)>1,s=s+1))): if(k==2000,k=0):print1(k","))

%Y Cf. A070298.

%K nonn

%O 0,1

%A _Amarnath Murthy_, May 10 2002

%E Corrected and extended by _Ralf Stephan_, Mar 22 2003