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

1,3

Comments

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

Links

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

Example

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).

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 *)

Crossrefs

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

Sequence in context: A342464 A061342 A104639 * A161223 A145672 A175024

Adjacent sequences: A260701 A260702 A260703 * A260705 A260706 A260707

Keyword

nonn,base

Author

Michel Lagneau, Nov 17 2015

Status

approved