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A260703
Numbers having at least two distinct divisors with the property that the reversal of one is equal to the other.
2
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
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
KEYWORD
nonn,base
AUTHOR
Michel Lagneau, Nov 17 2015
STATUS
approved