A035132 Nonsquarefree palindromes.

4, 8, 9, 44, 88, 99, 121, 171, 212, 232, 242, 252, 272, 292, 333, 343, 363, 404, 414, 424, 444, 464, 484, 525, 575, 585, 616, 636, 656, 666, 676, 686, 696, 747, 808, 828, 848, 868, 888, 909, 999, 1331, 1881, 2112, 2332, 2552, 2662, 2772, 2992, 3663, 3773

Offset: 1

Author

Patrick De Geest, Nov 15 1998

Keywords

• nonn
• base

Examples

			4114 = 2 * 11^2 * 17.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Squarefree.

Crossrefs

Intersection of A002113 and A013929.

Supersequence of A077572.

Cf. A005117, A035133, A071251, A075804 (first differences).

Programs

Mathematica

sfQ[n_]:=Max[Transpose[FactorInteger[n]][[2]]]>1; palQ[n_]:=FromDigits[Reverse[IntegerDigits[n]]]==n; Select[Range[2,3776],sfQ[#] && palQ[#] &] (* Jayanta Basu, May 12 2013 *)
Select[Range[4000], PalindromeQ[#] && !SquareFreeQ[#] &] (* Amiram Eldar, Feb 25 2021 *)

Python

from itertools import product
from sympy.ntheory.factor_ import core
def palsthru(maxdigits):
  midrange = [[""], [str(i) for i in range(10)]]
  for digits in range(1, maxdigits+1):
    for p in product("0123456789", repeat=digits//2):
      left = "".join(p)
      if len(left) and left[0] == '0': continue
      for middle in midrange[digits%2]: yield int(left+middle+left[::-1])
def okpal(p): return p > 3 and core(p, 2) != p
print(list(filter(okpal, palsthru(4)))) # Michael S. Branicky, Apr 08 2021