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A161955
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TITO2(n): The operation A161594 in binary, digit-reversals carried out in base 2.
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2
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1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 11, 3, 13, 7, 15, 1, 17, 9, 19, 5, 21, 11, 23, 3, 19, 13, 27, 7, 29, 15, 31, 1, 57, 17, 49, 9, 37, 19, 33, 5, 41, 21, 43, 11, 45, 23, 47, 3, 35, 19, 51, 13, 53, 27, 65, 7, 105, 29, 59, 15, 61, 31, 63, 1, 59, 57, 67, 17, 117, 49, 71, 9, 73, 37, 105, 19, 109
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| The TITO function in binary: Represent n as a product of its prime factors in binary.
Revert the binary digits of each of these factors, then multiply them with
the same multiplicities as in n--so the base-2 representation does not effect
the exponents in the canonical prime factorization. Reverse the product in binary to get a(n).
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LINKS
| T. Khovanova, Turning Numbers Inside Out [From Tanya Khovanova (tanyakh(AT)yahoo.com), Jul 07 2009]
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FORMULA
| a(n) = A030101(A162742(n)) - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 03 2009
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EXAMPLE
| To calculate TITO2(n=99): 99 = 3^3*11. Prime factors 3 and 11 in binary are 11 and
1011 correspondingly. Reversing those numbers we get 11 and 1101. The product with
multiplicities is the binary product of 11*11*1101 = 1110101. Reversing that we
get 1010111, which corresponds to 87. Hence a(99) = 87.
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MATHEMATICA
| reverseBinPower[{n_, k_}] := FromDigits[Reverse[IntegerDigits[n, 2]], 2]^k fBin[n_] := FromDigits[ Reverse[IntegerDigits[ Times @@ Map[reverseBinPower, FactorInteger[n]], 2]], 2] Table[fBin[n], {n, 200}]
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CROSSREFS
| Cf. A161594
Sequence in context: A145799 A098985 A072963 * A000265 A106617 A040026
Adjacent sequences: A161952 A161953 A161954 * A161956 A161957 A161958
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KEYWORD
| base,nonn
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AUTHOR
| Tanya Khovanova (tanyakh(AT)yahoo.com), Jun 22 2009
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EXTENSIONS
| Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 03 2009
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