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%I #11 Sep 03 2017 21:42:42
%S 1,2,3,4,5,7,9,12,16,18,21,28,30,37,43,51,53,59,66,92,103,150,188,189,
%T 235,239,312,351,396,400,493,593,628,751,947,954,1283,1433,1632,2063,
%U 2074,2088,2446,2629,3143,3582,3952,4008,4121,4602,5803,6046,6323,6899
%N Records transform of A252665.
%C See a-file "Records and first positions of records in A252665" in that sequence for more information. - _Michael De Vlieger_, Sep 03 2017
%H Michael De Vlieger, <a href="/A291833/b291833.txt">Table of n, a(n) for n = 1..76</a>
%e A252665(n) for 1 <= n <= 24 is {1, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 4, 1, 2, 2, 5, 1, 4, 1, 4, 2, 2, 1, 7}; the records are {1, 2, 3, 4, 5, 7}, thus these are the first 6 terms of this sequence.
%t f[n_, i_, t_] := b[n, i, t] = If[n == 1, 1, If[t == 1, Boole[n <= i],
%t Sum[f[n/d, d, t - 1], {d, Select[Divisors@ n, # <= i &]}]]]; Union@ FoldList[Max, Array[f[#, #, 5] &, 10^5]] (* _Michael De Vlieger_, Sep 03 2017, after _Alois P. Heinz_ at A218320 *)
%Y Cf. A033833, A252665, A291834.
%K nonn
%O 1,2
%A _Michael De Vlieger_, Sep 03 2017
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