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A358513 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).

%I A358513 #22 Dec 29 2022 09:48:42
%S A358513 1,2,4,8,12,24,48,88,220,176,132,968,264,396,528,792,1320,1584,2640,
%T A358513 3960,5808,5544,8712,14520,11088,24024,21780,36036,40656,39996,53328,
%U A358513 87120,60984,72072,205128,132132,121968,144144,293304,199980,266640,439956,264264,360360,733260,396396,660660,799920
%N A358513 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 A358513 1 has no divisors that can be written in the form m + reverse(m), so a(0) = 1.
%e A358513 2 has only the divisor 2 which is written 2 = 1 + reverse(1), so a(1) = 2.
%e A358513 3 has no divisors that can be written in the form m + reverse(m).
%e A358513 4 has divisors 1, 2, 4 but only 2 = 1 + reverse(1) and 4 = 2 + reverse(2), so a(2) = 4.
%e A358513 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 A358513 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 A358513 rev:= proc(n) local L,i; L:= convert(n,base,10); add(L[-i]*10^(i-1),i=1..nops(L)) end proc:
%p A358513 S:= select(`<=`, map(t -> t + rev(t), {$1..10^6}),10^6):
%p A358513 V:= Array(0..49): count:= 0:
%p A358513 for n from 1 to 10^6 while count < 50 do
%p A358513   v:= nops(numtheory:-divisors(n) intersect S);
%p A358513   if v <= 49 and V[v] = 0 then
%p A358513      count:= count+1; V[v]:= n;
%p A358513   fi
%p A358513 od:
%p A358513 convert(V,list); # _Robert Israel_, Dec 28 2022
%o A358513 (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 A358513 Cf. A067032, A067030.
%K A358513 nonn,base
%O A358513 0,2
%A A358513 _Marius A. Burtea_, Dec 04 2022
%E A358513 More terms from _Robert Israel_, Dec 28 2022