%I A076537
%S A076537 5,12,13,14,23,25,27,31,34,38,40,41,42,44,57,58,59,61,63,64,65,80,82,
%T A076537 84,85,86,88,90,94,96,97,100,101,103,107,109,111,113,115,117,119,138,
%U A076537 139,140,142,144,145,146,148,150,151,152,173,175,176,177,179,181,183
%N A076537 Map positive rational numbers to positive integers by diagonal method 
               using c(p,q) = (p + q - 2) * (p + q - 1) / 2 + p where p and q are 
               positive integers. a(n) is an increasing sequence including all c(p,
               q) where GCD(p,q) > 1.
%e A076537 a(1) = c(2,2) = (2 + 2 - 2) * (2 + 2 - 1) / 2 + 2 = 5 because GCD(2,2) 
               = 2 > 1. a(2) = c(2,4) = (2 + 4 - 2) * (2 + 4 - 1) / 2 + 2 = 12 because 
               GCD(2,4) = 2 > 1.
%o A076537 (PARI) a(n)=if(n<1,0,n=a(n-1); until(1<gcd(n-binomial(floor(1/2+sqrt(2 
               *n)),2),binomial(floor(3/2+sqrt(2*n)),2)-n+1),n++); n)
%Y A076537 Sequence in context: A066326 A015242 A009415 this_sequence A110134 A014156 
               A114073
%Y A076537 Adjacent sequences: A076534 A076535 A076536 this_sequence A076538 A076539 
               A076540
%K A076537 nonn
%O A076537 1,1
%A A076537 Robert A. Stump (bee_ess107(AT)msn.com), Oct 18 2002