A338927 - OEIS

%I #10 Nov 15 2020 22:33:58

%S 1,4,6,8,12,24,36,48,72,96,144,192,240,288,384,432,576,864,1152,1440,

%T 1728,2304,2880,3456,4320,4608,5184,5760,6912,8640,10368,11520,13824,

%U 17280,20736,23040,25920,27648,34560,41472,51840,62208,69120,82944

%N Locations of records in A338565.

%C The first term divisible by 3 is a(3)=6.

%C The first term divisible by 5 is a(13)=240.

%C The first term divisible by 11 is a(48)=190080.

%e a(3) = 6 is in the sequence because A338565(6) = 3 is greater than A338565(n) for n < 6.

%p ispali:= proc(n) local L;

%p   L:= convert(n,base,10);

%p   evalb(L = ListTools:-Reverse(L))

%p end proc:

%p N:= 200000: # for terms <= N

%p Palis:= select(ispali, {$2..N}):

%p A338565:= Vector(N):

%p A338565[1]:= 1:

%p R:= 1: bestv:= 1:

%p A[1]:= 1:

%p for n from 2 to N do

%p   A[n]:=  add(A[n/d], d= numtheory:-divisors(n) intersect Palis);

%p     if A[n] > bestv then bestv:= A[n]; R:= R, n

%p od:

%p R;

%t Block[{a, s}, a[n_] := If[n == 1, n, Sum[If[(d < n && PalindromeQ[n/d]), a[d], 0], {d, Divisors[n]}]]; s = Array[a, 10^4]; Map[FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]] ] (* _Michael De Vlieger_, Nov 15 2020 *)

%Y Cf. A338565, A328928.

%K nonn

%O 1,2

%A _Robert Israel_, Nov 15 2020