A260704 Number of pairs of distinct divisors of A260703(n) having the property that the reversal of one is equal to the other.

1, 1, 2, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 3, 1, 1, 1, 1, 2, 3, 1, 2, 1, 2, 2, 2, 1, 2, 1, 1, 4, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 3, 1, 1, 1, 1, 1, 2, 4, 1, 1, 2, 2, 3, 1, 1, 1, 2, 2, 1, 4, 1, 1, 1, 2, 1, 1, 4, 1, 1, 1, 2, 2, 2, 1, 3, 1, 2, 3, 2, 1, 3, 2, 1, 3

Offset: 1

Author

Michel Lagneau, Nov 17 2015

Keywords

• nonn
• base

Comments

A260703: numbers having at least two divisors such that the reversal of one is equal to the other.

Examples

			a(9)=3 because A260703(9) = 336 and the set of the divisors of 336, {1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336} contains 3 pairs (12, 21), (24, 42) and (48, 84) with the property: 21 = reversal(12), 42 = reversal(24) and 84 = reversal(48).
		

Links

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

Crossrefs

Cf. A000005, A027750, A083815, A260703, A260705.

Programs

Maple

with(numtheory):nn:=5000:
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, `,it):
    else fi:
od:

Mathematica

f[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]; f /@ Range@ 3000 /. 0 -> Nothing (* Michael De Vlieger, Nov 17 2015 *)