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.

84, 168, 336, 1008, 3024, 5544, 11088, 16632, 33264, 49896, 99792, 182952, 365904, 249480, 498960, 1097712, 2162160, 3359664, 1846152, 3027024, 5538456, 6054048, 9081072, 9230760, 14270256, 19891872, 20307672, 25197480, 33297264, 45405360, 55135080, 71351280

Offset

1,1

Comments

It seems that a(n)==0 (mod 84).

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

Links

Lars Blomberg, Table of n, a(n) for n = 1..75.

Example

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).

Maple

with(numtheory):nn:=10^8:
for n from 1 to 16 do:
ii:=0:
for m from 1 to nn while(ii=0) do:
it:=0:d:=divisors(m):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=n
    then
    ii:=1:printf("%d %d \n", n, m):
    else fi:
od:
od:

Prog

(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; }
a(n) = {k=1; while (nbrp(divisors(k)) != n, k++); k; } \\ Michel Marcus, Dec 27 2015

Crossrefs

Cf. A000005, A027750, A083815, A206703, A260704.

Sequence in context: A044254 A044635 A273018 * A295596 A287118 A306514

Adjacent sequences: A260702 A260703 A260704 * A260706 A260707 A260708

Keyword

nonn,base

Author

Michel Lagneau, Nov 17 2015

Extensions

a(14)-a(15) corrected by Lars Blomberg, Dec 27 2015

a(7), a(19), a(20) corrected and a(21)-a(32) added by Lars Blomberg, Jan 04 2016

Status

approved