A076963 - OEIS

%I #18 Jun 09 2024 09:06:11

%S 1,2,3,4,9,10,21,22,27,28,45,52,63,64,105,128,135,136,165,182,225,256,

%T 315,352,525,544,585,608,675,704,945,1144,1575,2288,2835,2992,4095,

%U 5984,5985,7072,7245,7904,8085,9568,9765,10208,11025,11968,12285,23936,25935

%N Lexicographically earliest increasing sequence of relatively prime numbers with nondecreasing number of divisors. a(1) = 1, tau(a(n+1)) >= tau(a(n)) and GCD(a(n),a(n+1)) = 1.

%C It appears that a(n) is divisible by 2 iff n is odd, and by 3 iff n >= 2 is even. - _Robert Israel_, Jun 08 2024

%H Robert Israel, <a href="/A076963/b076963.txt">Table of n, a(n) for n = 0..200</a>

%p R:= 1: d:= 1: count:= 1: x:= 1:

%p for i from 2 while count < 80 do

%p   if igcd(i,x) = 1 then

%p     di:= numtheory:-tau(i);

%p     if di >= d then x:= i; d:= di; R:= R,i; count:= count+1 fi

%p   fi

%p od:

%p R; # _Robert Israel_, Jun 07 2024

%K nonn

%O 0,2

%A _Amarnath Murthy_, Oct 21 2002

%E More terms from _Sascha Kurz_, Jan 22 2003

%E Definition clarified by _Robert Israel_, Jun 07 2024