A254438 Natural numbers k such that k is a multiple of its number of "feasible" partitions.

1, 2, 3, 4, 6, 8, 10, 11, 12, 13, 28, 30, 33, 36, 38, 39, 40, 72, 92, 110, 114, 116, 118, 119, 120, 121, 330, 350, 355, 357, 360, 362, 363, 364, 1086, 1088, 1090, 1091, 1092, 1093, 3248, 3270, 3273, 3276, 3278, 3279, 3280, 9792, 9828, 9830, 9834, 9836, 9838, 9839, 9840, 9841, 29376, 29512, 29515, 29517, 29520, 29522, 29523, 29524

Offset

1,2

Comments

This sequence lists the natural numbers k that are divisible by A254296(k).

Links

Table of n, a(n) for n=1..64.

Md Towhidul Islam & Md Shahidul Islam, Number of Partitions of an n-kilogram Stone into Minimum Number of Weights to Weigh All Integral Weights from 1 to n kg(s) on a Two-pan Balance, arXiv:1502.07730 [math.CO], 2015.

Example

For n=1,2,3, A254296(n)=1, so they are in the sequence.
For n=4,6,8,10, A254296(n)=2, so they are in the sequence.
For n=5,9, A254296(n)=2, so they are not in the sequence.

Mathematica

(* This program is not suitable to compute a large number of terms. *)
okQ[v_] := Module[{s=0}, For[i=1, i <= Length[v], i++, If[v[[i]] > 2s+1, Return[False], s += v[[i]]]]; Return[True]];
b[n_] := b[n] = With[{k = Ceiling[Log[3, 2 n]]}, Select[Reverse /@ IntegerPartitions[n, {k}], okQ] // Length];
Reap[Do[If[Divisible[k, b[k]], Print[k]; Sow[k]], {k, 1, 120}]][[2, 1]] (* Jean-François Alcover, Nov 03 2018 *)

Crossrefs

Cf. A254296, A254430, A254431, A254432, A254433, A254435, A254436, A254437, A254438, A254439, A254440.

Sequence in context: A097274 A322572 A375564 * A121539 A257457 A122138

Adjacent sequences: A254435 A254436 A254437 * A254439 A254440 A254441

Keyword

nonn

Author

Md. Towhidul Islam, Mar 01 2015

Extensions

a(48)-a(64) added by Md. Towhidul Islam, Apr 18 2015

Status

approved