A291833 Records transform of A252665.

1, 2, 3, 4, 5, 7, 9, 12, 16, 18, 21, 28, 30, 37, 43, 51, 53, 59, 66, 92, 103, 150, 188, 189, 235, 239, 312, 351, 396, 400, 493, 593, 628, 751, 947, 954, 1283, 1433, 1632, 2063, 2074, 2088, 2446, 2629, 3143, 3582, 3952, 4008, 4121, 4602, 5803, 6046, 6323, 6899

Offset

1,2

Comments

See a-file "Records and first positions of records in A252665" in that sequence for more information. - Michael De Vlieger, Sep 03 2017

Links

Michael De Vlieger, Table of n, a(n) for n = 1..76

Example

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.

Mathematica

f[n_, i_, t_] := b[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[#, #, 5] &, 10^5]] (* Michael De Vlieger, Sep 03 2017, after Alois P. Heinz at A218320 *)

Crossrefs

Cf. A033833, A252665, A291834.

Sequence in context: A096814 A039861 A039877 * A272691 A192433 A189083

Adjacent sequences: A291830 A291831 A291832 * A291834 A291835 A291836

Keyword

nonn

Author

Michael De Vlieger, Sep 03 2017

Status

approved