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A229970 Numbers n such that the product of their proper divisors is a palindrome > 1 and not equal to n. 2
4, 9, 25, 49, 121, 212, 1001, 2636, 10201, 17161, 22801, 32761, 36481, 97969, 110011, 124609, 139129, 146689, 528529, 573049, 619369, 635209, 844561, 863041, 1100011, 10100101, 11000011, 101000101, 106110601, 110000011, 110271001, 112381201, 127938721, 130210921 (list; graph; refs; listen; history; text; internal format)
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

Cf. A007956.

Sequence in context: A052043 A188836 A030146 * A038771 A158146 A158147

Adjacent sequences:  A229967 A229968 A229969 * A229971 A229972 A229973

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

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Last modified August 18 02:34 EDT 2022. Contains 356204 sequences. (Running on oeis4.)