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).

1, 2, 4, 8, 12, 24, 48, 88, 220, 176, 132, 968, 264, 396, 528, 792, 1320, 1584, 2640, 3960, 5808, 5544, 8712, 14520, 11088, 24024, 21780, 36036, 40656, 39996, 53328, 87120, 60984, 72072, 205128, 132132, 121968, 144144, 293304, 199980, 266640, 439956, 264264, 360360, 733260, 396396, 660660, 799920

Offset

0,2

Links

Table of n, a(n) for n=0..47.

Example

1 has no divisors that can be written in the form m + reverse(m), so a(0) = 1.
2 has only the divisor 2 which is written 2 = 1 + reverse(1), so a(1) = 2.
3 has no divisors that can be written in the form m + reverse(m).
4 has divisors 1, 2, 4 but only 2 = 1 + reverse(1) and 4 = 2 + reverse(2), so a(2) = 4.
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).
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.

Maple

rev:= proc(n) local L, i; L:= convert(n, base, 10); add(L[-i]*10^(i-1), i=1..nops(L)) end proc:
S:= select(`<=`, map(t -> t + rev(t), {$1..10^6}), 10^6):
V:= Array(0..49): count:= 0:
for n from 1 to 10^6 while count < 50 do
  v:= nops(numtheory:-divisors(n) intersect S);
  if v <= 49 and V[v] = 0 then
     count:= count+1; V[v]:= n;
  fi
od:
convert(V, list); # Robert Israel, Dec 28 2022

Prog

(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;

Crossrefs

Cf. A067032, A067030.

Sequence in context: A343014 A097942 A354541 * A004653 A115386 A306491

Adjacent sequences: A358510 A358511 A358512 * A358514 A358515 A358516

Keyword

nonn,base

Author

Marius A. Burtea, Dec 04 2022

Extensions

More terms from Robert Israel, Dec 28 2022

Status

approved