A081532 Triangle read by rows: let m be smallest number with n divisors, then row n gives divisors of m.

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, 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, 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

Offset: 1

Author

Amarnath Murthy, Mar 28 2003

Keywords

• nonn
• tabl

Examples

			Triangle begins
1;
1,2;
1,2,4;
1,2,3,6;
1,2,4,8,16;
1,2,3,4,6,12;
...
		

Links

• Michel Marcus, Rows n=1..200 of triangle, flattened
• Eric Weisstein's World of Mathematics, Divisor

Crossrefs

Leading diagonal is A005179. Cf. A000005, A081533.

Programs

Mathematica

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 *)

Formula

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

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

Extensions

More terms from Sam Alexander, Oct 21 2003

More terms from Michel Marcus, Nov 15 2020