A081533 -id:A081533 - cp's OEIS frontend

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

Amarnath Murthy, Mar 28 2003

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

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

Leading diagonal is A005179. Cf. A000005, A081533.

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 *)

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.

More terms from Sam Alexander, Oct 21 2003

More terms from Michel Marcus, Nov 15 2020

A256259 Sum of divisors of the minimal numbers (A007416).

Original entry on oeis.org

1, 3, 7, 12, 28, 31, 60, 91, 124, 168, 127, 360, 403, 546, 508, 744, 1170, 1651, 2418, 2880, 2821, 3048, 2047, 4368, 3751, 5952, 9360, 9906, 8188, 12493, 8191, 19344, 15367, 22568, 22506, 24384, 28800, 26611, 39312, 32764, 51181, 59520, 49128, 79248, 99944, 92202, 112320, 116281, 106483, 160797

Offset: 1

Omar E. Pol, Apr 20 2015

nonn

Has a symmetric representation in the same way as A000203 and all its subsequences.

Amiram Eldar, Table of n, a(n) for n = 1..10000 (calculated from the b-file at A007416)

Cf. A000203, A005179, A007416, A007626, A053212, A063072, A081533, A237271, A237593.

(* The d-th element in list minDiv[n, b] is the smallest numbers k<=n with exactly d<=b divisors, otherwise it is zero. Computation stops as soon as either inequality fails. *)
minDiv[n_, b_] :=
Module[{list = Array[0 &, b], k = 1, d},
  While[k <= n, d = DivisorSigma[0, k];
   If[d <= b && list[[d]] == 0, list[[d]] = k];
   If[d <= b, k++, k = n + 2]]; list]
a256259[n_, b_] :=
Map[DivisorSigma[1, #] &, Sort[Select[minDiv[n, b], # != 0 &]]]
a256259[100000, 300] (* computes the first 60 elements of the sequence *)
(* Hartmut F. W. Hoft, Apr 27 2015 *)

a(n) = A000203(A007416(n)).

cp's OEIS Frontend

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

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