A260703 Numbers having at least two distinct divisors with the property that the reversal of one is equal to the other.

84, 162, 168, 216, 252, 255, 270, 324, 336, 403, 420, 432, 486, 504, 510, 540, 574, 588, 648, 672, 736, 756, 765, 806, 810, 840, 864, 924, 972, 976, 1008, 1020, 1080, 1092, 1134, 1148, 1176, 1207, 1209, 1260, 1275, 1296, 1300, 1344, 1350, 1425, 1428, 1458

Offset

1,1

Comments

The corresponding numbers of pairs of divisors having this property are 1, 1, 2, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 3,... (see A260704).

Links

Michel Lagneau, Table of n, a(n) for n = 1..10000

Example

336 is in the sequence because the set of its divisors {1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336} contains at least two distinct divisors with the property that the reversal of one is equal to the other. This set contains 3 pairs (12, 21), (24, 42) and (48, 84) with the property 21 = reversal(12), 42 = reversal(24) and 84 = reversal(48).

Maple

with(numtheory):nn:=20000:
for n from 1 to nn do:
it:=0:d:=divisors(n):d0:=nops(d):
  for i from 1 to d0 do:
   dd:=d[i]:y:=convert(dd, base, 10):n1:=length(dd):
   s:=sum('y[j]*10^(n1-j)', 'j'=1..n1):
    for k from i+1 to d0 do:
     if s=d[k]
     then
     it:=it+1:
     else fi:
    od:
    od:
    if it>0
    then
    printf(`%d, `, n):
    else fi:
od:

Mathematica

fQ[n_] := Block[{d = Select[Divisors@ n, IntegerLength@ # > 1 &], palQ, r}, palQ[x_] := Reverse@ # == # &@ IntegerDigits@ x; r = FromDigits@ Reverse@ IntegerDigits@ # & /@ d; Length@ Select[Intersection[d, r], ! palQ@ # &] >= 2]; Select[Range@ 1500, fQ] (* Michael De Vlieger, Nov 17 2015 *)

Crossrefs

Cf. A000005, A027750, A083815, A260704, A260705.

Sequence in context: A341128 A055712 A066292 * A044254 A044635 A273018

Adjacent sequences: A260700 A260701 A260702 * A260704 A260705 A260706

Keyword

nonn,base

Author

Michel Lagneau, Nov 17 2015

Status

approved