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%I #5 Sep 17 2017 22:53:21
%S 1,2,3,4,5,7,9,11,15,16,20,25,27,33,36,46,50,53,77,86,118,145,158,173,
%T 174,184,224,270,282,304,330,422,522,625,656,820,881,899,1030,1218,
%U 1276,1416,1529,1590,1722,2012,2106,2161,2369,2478,2994,3132,3361,3484
%N Records transform of A218320.
%e A218320(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_] := f[n, i, t] = If[n == 1, 1, If[t == 1, Boole[n <= i], Sum[f[n/d, d, t - 1], {d, Select[Divisors@ n, # <= i &]}]]]; Union@ FoldList[Max, Array[f[#, #, 4] &, 10^5]] (* _Michael De Vlieger_, Sep 06 2017, after _Alois P. Heinz_ at A218320 *)
%Y Cf. A033833, A218320.
%K nonn
%O 1,2
%A _Michael De Vlieger_, Sep 06 2017
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