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

1,3

Links

Michel Marcus, Rows n=1..200 of triangle, flattened

Eric Weisstein's World of Mathematics, Divisor

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.

Example

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

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 *)

Crossrefs

Leading diagonal is A005179. Cf. A000005, A081533.

Sequence in context: A104778 A356184 A292477 * A174843 A253572 A141539

Adjacent sequences: A081529 A081530 A081531 * A081533 A081534 A081535

Keyword

nonn,tabl

Author

Amarnath Murthy, Mar 28 2003

Extensions

More terms from Sam Alexander, Oct 21 2003

More terms from Michel Marcus, Nov 15 2020

Status

approved