A242416 Numbers whose prime factorization viewed as a tuple of nonzero powers is not palindromic.

12, 18, 20, 24, 28, 40, 44, 45, 48, 50, 52, 54, 56, 60, 63, 68, 72, 75, 76, 80, 84, 88, 92, 96, 98, 99, 104, 108, 112, 116, 117, 120, 124, 132, 135, 136, 140, 144, 147, 148, 150, 152, 153, 156, 160, 162, 164, 168, 171, 172, 175, 176, 180, 184, 188, 189, 192, 200

Offset: 1

Author

Antti Karttunen, May 29 2014

Keywords

• nonn

Comments

These are terms that appear in 2-cycles of permutation A069799.

Complement of A242414.

Examples

			12 = p_1^2 * p_2^1 is present, as (2,1) is not a palindrome.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Complement: A242414.

A subsequence of A059404, from which this differs for the first at n=23, as 90 = A059404(23) is not member of this sequence, as the exponents in the prime factorization of 90 = 2^1 * 3^2 * 5^1 form a palindrome, even though 90 is not a power of a squarefree number.

Cf. A069799.

Programs

Maple

q:= n-> (l-> is(n<>mul(l[i, 1]^l[-i, 2], i=1..nops(l))))(sort(ifactors(n)[2])):
select(q, [$1..200])[];  # Alois P. Heinz, Feb 04 2022

Mathematica

Select[Range[200], !PalindromeQ[FactorInteger[#][[All, 2]]]&] (* Jean-François Alcover, Feb 09 2025 *)