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%I #27 Nov 03 2018 18:47:05
%S 1,2,3,4,6,8,10,11,12,13,28,30,33,36,38,39,40,72,92,110,114,116,118,
%T 119,120,121,330,350,355,357,360,362,363,364,1086,1088,1090,1091,1092,
%U 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
%N Natural numbers k such that k is a multiple of its number of "feasible" partitions.
%C This sequence lists the natural numbers k that are divisible by A254296(k).
%H Md Towhidul Islam & Md Shahidul Islam, <a href="http://arxiv.org/abs/1502.07730">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</a>, arXiv:1502.07730 [math.CO], 2015.
%e For n=1,2,3, A254296(n)=1, so they are in the sequence.
%e For n=4,6,8,10, A254296(n)=2, so they are in the sequence.
%e For n=5,9, A254296(n)=2, so they are not in the sequence.
%t (* This program is not suitable to compute a large number of terms. *)
%t okQ[v_] := Module[{s=0}, For[i=1, i <= Length[v], i++, If[v[[i]] > 2s+1, Return[False], s += v[[i]]]]; Return[True]];
%t b[n_] := b[n] = With[{k = Ceiling[Log[3, 2 n]]}, Select[Reverse /@ IntegerPartitions[n, {k}], okQ] // Length];
%t Reap[Do[If[Divisible[k, b[k]], Print[k]; Sow[k]], {k, 1, 120}]][[2, 1]] (* _Jean-François Alcover_, Nov 03 2018 *)
%Y Cf. A254296, A254430, A254431, A254432, A254433, A254435, A254436, A254437, A254438, A254439, A254440.
%K nonn
%O 1,2
%A _Md. Towhidul Islam_, Mar 01 2015
%E a(48)-a(64) added by _Md. Towhidul Islam_, Apr 18 2015
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