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

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Squarefree.

Example

4114 = 2 * 11^2 * 17.

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 *)

Prog

(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

Crossrefs

Intersection of A002113 and A013929.

Supersequence of A077572.

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

Sequence in context: A076966 A360758 A237607 * A077572 A239520 A083807

Adjacent sequences: A035129 A035130 A035131 * A035133 A035134 A035135

Keyword

nonn,base

Author

Patrick De Geest, Nov 15 1998

Status

approved