

A242414


Numbers whose prime factorization viewed as a tuple of nonzero powers is palindromic.


20



1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 46, 47, 49, 51, 53, 55, 57, 58, 59, 61, 62, 64, 65, 66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 81, 82, 83, 85, 86, 87, 89, 90, 91, 93, 94, 95, 97, 100
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OFFSET

1,2


COMMENTS

The fixed points of permutation A069799.
Differs from its subsequence, A072774, Powers of squarefree numbers, for the first time at n=68, as here a(68) = 90 is included, as 90 = p_1^1 * p_2^2 * p_3^1 has a palindromic tuple of exponents, even although not all of them are identical.
Differs from its another subsequence, A236510, in that, although numbers like 42 = 2^1 * 3^1 * 5^0 * 7^1, with a nonpalindromic exponenttuple (1,1,0,1) are excluded from A236510, it is included in this sequence, because here only the nonzero exponents are considered, and (1,1,1) is a palindrome.
Differs from A085924 in that as that sequence is subtly basedependent, it excludes 1024 (= 2^10), as then the only exponent present, 10, and thus also its concatenation, "10", is not a palindrome when viewed in decimal base. On the contrary, here a(691) = 1024.


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000


EXAMPLE

As 1 has an empty factorization, (), which also is a palindrome, 1 is present.
As 42 = 2 * 3 * 7 = p_1^1 * p_2^1 * p_4^1, and (1,1,1) is palindrome, 42 is present.
As 90 = 2 * 9 * 5 = p_1^1 * p_2^2 * p_3^1, and (1,2,1) is palindrome, 90 is present.
Any prime power (A000961) is present, as such numbers have a factorization p^e (e >= 1), and any singleton sequence (e) by itself forms a palindrome.


PROG

(Scheme, with Antti Karttunen's IntSeqlibrary)
(define A242414 (FIXEDPOINTS 1 1 A069799))


CROSSREFS

Fixed points of A069799.
Complement: A242416.
A000961, A072774 and A236510 are subsequences.
Cf. A242418, A085924.
Sequence in context: A317101 A304449 A085924 * A072774 A062770 A236510
Adjacent sequences: A242411 A242412 A242413 * A242415 A242416 A242417


KEYWORD

nonn


AUTHOR

Antti Karttunen, May 30 2014


STATUS

approved



