A081532 - OEIS

%I #19 Nov 16 2020 03:40:39

%S 1,1,2,1,2,4,1,2,3,6,1,2,4,8,16,1,2,3,4,6,12,1,2,4,8,16,32,64,1,2,3,4,

%T 6,8,12,24,1,2,3,4,6,9,12,18,36,1,2,3,4,6,8,12,16,24,48,1,2,4,8,16,32,

%U 64,128,256,512,1024,1,2,3,4,5,6,10,12,15,20,30,60,1,2,4,8,16,32,64,128,256,512,1024,2048,4096

%N Triangle read by rows: let m be smallest number with n divisors, then row n gives divisors of m.

%H Michel Marcus, <a href="/A081532/b081532.txt">Rows n=1..200 of triangle, flattened</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Divisor.html">Divisor</a>

%F T(n,k) = k-th divisor of smallest number having exactly n divisors, 1<=k<=n.

%F T(n,1) = 1, T(n,n) = A005179(n); A000005(T(n,n)) = n.

%e Triangle begins

%e 1;

%e 1,2;

%e 1,2,4;

%e 1,2,3,6;

%e 1,2,4,8,16;

%e 1,2,3,4,6,12;

%e ...

%t Function[s, Map[Lookup[s, #] &, Range[First@ Complement[Range@ Max@ #, #] - 1]] &@ Keys@ s]@ Map[Divisors@ First@ # &, KeySort@ PositionIndex@ Array[DivisorSigma[0, #] &, 5000]] // Flatten (* _Michael De Vlieger_, Nov 15 2020 *)

%Y Leading diagonal is A005179. Cf. A000005, A081533.

%K nonn,tabl

%O 1,3

%A _Amarnath Murthy_, Mar 28 2003

%E More terms from _Sam Alexander_, Oct 21 2003

%E More terms from _Michel Marcus_, Nov 15 2020