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A242414
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Numbers whose prime factorization viewed as a tuple of nonzero powers is palindromic.
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26
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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
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1,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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