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A242414 Numbers whose prime factorization viewed as a tuple of nonzero powers is palindromic. 24
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 (list; graph; refs; listen; history; text; internal format)
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 non-palindromic exponent-tuple (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 base-dependent, 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 IntSeq-library)

(define A242414 (FIXED-POINTS 1 1 A069799))

CROSSREFS

Fixed points of A069799.

Complement: A242416.

A000961, A072774 and A236510 are subsequences.

Cf. A242418, A085924.

Sequence in context: A304449 A360247 A085924 * A072774 A062770 A359889

Adjacent sequences: A242411 A242412 A242413 * A242415 A242416 A242417

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 30 2014

STATUS

approved

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Last modified February 8 20:00 EST 2023. Contains 360152 sequences. (Running on oeis4.)