A244411 Nonprimes n such that the product of its divisors is a palindrome.

1, 4, 22, 26, 49, 111, 121, 202, 1001, 1111, 2285, 10001, 10201, 11111, 100001, 1000001, 1001001, 1012101, 1100011, 1101011, 1109111, 1111111, 3069307, 10000001, 12028229, 12866669, 100000001, 101000101, 110000011, 110091011, 200010002, 10000000001, 10011111001

Offset: 1

Author

Derek Orr, Jun 27 2014

Keywords

• nonn
• base
• hard

Comments

Primes trivially satisfy this property and are therefore not included in the sequence.

Numbers n such that A136522(A007955(n)) = 1.

A number is in the intersection of A002778 and A001358 iff it is in this sequence.

a(31) > 2*10^8.

a(32) > 4*10^8. - Chai Wah Wu, Aug 25 2015

Examples

			The divisors of 26 are 1,2,13,26. And 1*2*13*26 = 676 is a palindrome. Thus 26 is a member of this sequence.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..47 (terms < 3.5*10^11)

Crossrefs

Cf. A007955, A136522, A028980, A002778, A001358.

Programs

PARI

rev(n)={r="";for(i=1,#digits(n),r=concat(Str(digits(n)[i]),r));return(eval(r))}
for(n=1,2*10^8,if(!isprime(n),d=divisors(n);ss=prod(j=1,#d,d[j]);if(ss==rev(ss),print1(n,", "))))

Python

import sympy
from sympy import isprime
from sympy import divisors
def rev(n):
  r = ""
  for i in str(n):
    r = i + r
  return int(r)
def a():
  for n in range(1,10**8):
    if not isprime(n):
      p = 1
      for i in divisors(n):
        p*=i
      if rev(p)==p:
        print(n,end=', ')
a()

Python

from sympy import divisor_count, sqrt
A244411_list = [1]
for n in range(1,10**5):
    d = divisor_count(n)
    if d > 2:
        q, r = divmod(d,2)
        s = str(n**q*(sqrt(n) if r else 1))
        if s == s[::-1]:
            A244411_list.append(n) # Chai Wah Wu, Aug 25 2015

Extensions

a(31) from Chai Wah Wu, Aug 25 2015

a(32)-a(33) from Giovanni Resta, Sep 20 2019