A358513 - OEIS

%I #22 Dec 29 2022 09:48:42

%S 1,2,4,8,12,24,48,88,220,176,132,968,264,396,528,792,1320,1584,2640,

%T 3960,5808,5544,8712,14520,11088,24024,21780,36036,40656,39996,53328,

%U 87120,60984,72072,205128,132132,121968,144144,293304,199980,266640,439956,264264,360360,733260,396396,660660,799920

%N a(n) is the smallest number whose divisors include exactly n that can be written in the form m + reverse(m), for some m (A067030).

%e 1 has no divisors that can be written in the form m + reverse(m), so a(0) = 1.

%e 2 has only the divisor 2 which is written 2 = 1 + reverse(1), so a(1) = 2.

%e 3 has no divisors that can be written in the form m + reverse(m).

%e 4 has divisors 1, 2, 4 but only 2 = 1 + reverse(1) and 4 = 2 + reverse(2), so a(2) = 4.

%e 5 and 7 have no divisors that can be written in the form m + reverse(m), and 6 only has the divisors 2 = 2 + reverse(2) and 6 = 3 + reverse(3).

%e 8 has divisors 1, 2, 4, 8 but only 2 = 1 + reverse(1), 4 = 2 + reverse(2) and 8 = 4 + reverse(4), so a(3) = 8.

%p rev:= proc(n) local L,i; L:= convert(n,base,10); add(L[-i]*10^(i-1),i=1..nops(L)) end proc:

%p S:= select(`<=`, map(t -> t + rev(t), {$1..10^6}),10^6):

%p V:= Array(0..49): count:= 0:

%p for n from 1 to 10^6 while count < 50 do

%p   v:= nops(numtheory:-divisors(n) intersect S);

%p   if v <= 49 and V[v] = 0 then

%p      count:= count+1; V[v]:= n;

%p   fi

%p od:

%p convert(V,list); # _Robert Israel_, Dec 28 2022

%o (Magma) rev:=func<n|Seqint(Reverse(Intseq(n)))>; f:=func<n|exists(c){s:s in [0..n]| n eq s+rev(s)}>; a:=[]; for n in [0..25] do k:=1; while #[d:d in Divisors(k)|f(d)] ne n do k:=k+1; end while; Append(~a,k); end for; a;

%Y Cf. A067032, A067030.

%K nonn,base

%O 0,2

%A _Marius A. Burtea_, Dec 04 2022

%E More terms from _Robert Israel_, Dec 28 2022