cp's OEIS Frontend

A260705 Least integer k such that the set of the divisors of k contains exactly n pairs of numbers having the following property: for each pair of two distinct divisors, the reversal of one is equal to the other.

%I A260705 #23 Jan 07 2016 14:36:15
%S A260705 84,168,336,1008,3024,5544,11088,16632,33264,49896,99792,182952,
%T A260705 365904,249480,498960,1097712,2162160,3359664,1846152,3027024,5538456,
%U A260705 6054048,9081072,9230760,14270256,19891872,20307672,25197480,33297264,45405360,55135080,71351280
%N A260705 Least integer k such that the set of the divisors of k contains exactly n pairs of numbers having the following property: for each pair of two distinct divisors, the reversal of one is equal to the other.
%C A260705 It seems that a(n)==0 (mod 84).
%C A260705 Additional terms with n > 75: a(77) = 15455984544, a(80) = 27719972280, a(83) = 22439977560, a(84) = 18479981520, a(86) = 28559971440. - _Lars Blomberg_, Jan 04 2016
%H A260705 Lars Blomberg, <a href="/A260705/b260705.txt">Table of n, a(n) for n = 1..75</a>.
%e A260705 a(4)=1008 because the set of the divisors {1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, 1008} contains 4 pairs (12, 21), (24, 42), (36, 63) and (48, 84) with the property 21 = reversal(12), 42 = reversal(24), 63 = reversal(36) and 84 = reversal(48).
%p A260705 with(numtheory):nn:=10^8:
%p A260705 for n from 1 to 16 do:
%p A260705 ii:=0:
%p A260705 for m from 1 to nn while(ii=0) do:
%p A260705 it:=0:d:=divisors(m):d0:=nops(d):
%p A260705   for i from 1 to d0 do:
%p A260705    dd:=d[i]:y:=convert(dd,base,10):n1:=length(dd):
%p A260705    s:=sum('y[j]*10^(n1-j)', 'j'=1..n1):
%p A260705     for k from i+1 to d0 do:
%p A260705      if s=d[k]
%p A260705      then
%p A260705      it:=it+1:
%p A260705      else fi:
%p A260705     od:
%p A260705     od:
%p A260705     if it=n
%p A260705     then
%p A260705     ii:=1:printf("%d %d \n",n,m):
%p A260705     else fi:
%p A260705 od:
%p A260705 od:
%o A260705 (PARI) nbr(vd) = {nb = 0; for (j=1, #vd, da = vd[j]; rda = eval(concat(Vecrev(Str(da)))); rrda = eval(concat(Vecrev(Str(rda)))); if ((da != rda) && vecsearch(vd,rda) && (da == rrda), nb++);); nb/2;}
%o A260705 a(n) = {k=1; while (nbrp(divisors(k)) != n, k++); k;} \\ _Michel Marcus_, Dec 27 2015
%Y A260705 Cf. A000005, A027750, A083815, A206703, A260704.
%K A260705 nonn,base
%O A260705 1,1
%A A260705 _Michel Lagneau_, Nov 17 2015
%E A260705 a(14)-a(15) corrected by _Lars Blomberg_, Dec 27 2015
%E A260705 a(7), a(19), a(20) corrected and a(21)-a(32) added by _Lars Blomberg_, Jan 04 2016