OFFSET
1,1
COMMENTS
Since the product of proper divisors must be > 1, these terms are necessarily composite. - Derek Orr, Apr 05 2015
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..62
EXAMPLE
The product of the proper divisors of 2636 is 6948496 (a palindrome). So, 2636 is a member of this sequence.
The product of the proper divisors of 8 is 8 (a palindrome) but equal to 8. So 8 is not in this sequence.
MAPLE
isA002113 := proc(n)
dgs := convert(n, base, 10) ;
for i from 1 to nops(dgs)/2 do
if op(i, dgs) <> op(-i, dgs) then
return false;
end if;
end do:
true ;
end proc:
for n from 4 do
if not isprime(n) then
ppd := A007956(n) ;
if n <> ppd and isA002113(ppd) then
printf("%d, ", n);
end if;
end if;
end do: # R. J. Mathar, Oct 09 2013
MATHEMATICA
palQ[n_] := Block[{d = IntegerDigits@ n}, d == Reverse@ d]; fQ[n_] := Block[{s = Times @@ Most@ Divisors@ n}, And[palQ@s, s > 1, s != n]]; Select[Range@ 1000000, CompositeQ@ # && fQ@ # &] (* Michael De Vlieger, Apr 06 2015 *)
PROG
(Python)
from sympy import divisors
def PD(n):
p = 1
for i in divisors(n):
if i != n:
p *= i
return p
def pal(n):
r = ''
for i in str(n):
r = i + r
return r == str(n)
{print(n, end=', ') for n in range(1, 10**4) if pal(PD(n)) and (PD(n)-1) and PD(n)-n}
## Simplified by Derek Orr, Apr 05 2015
(PARI) ispal(n)=Vecrev(n=digits(n))==n
is(n)=my(k=if(issquare(n, &k), k^numdiv(n)/n, n^(numdiv(n)/2-1))); k!=n && k>1 && ispal(k) \\ Charles R Greathouse IV, Oct 09 2013
(PARI) pal(n)=d=digits(n); Vecrev(d)==d
for(n=1, 10^6, D=divisors(n); p=prod(i=1, #D-1, D[i]); if(pal(p)&&p-1&&p-n, print1(n, ", "))) \\ Derek Orr, Apr 05 2015
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Derek Orr, Oct 04 2013
EXTENSIONS
a(14)-a(18) from R. J. Mathar, Oct 09 2013
a(19)-a(34) from Charles R Greathouse IV, Oct 09 2013
Definition edited by Derek Orr, Apr 05 2015
STATUS
approved