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Search: id:A064084
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| 1, 3, 7, 15, 31, 21, 127, 255, 511, 93, 2047, 105, 8191, 381, 217, 65535, 131071, 1533, 524287, 465, 889, 6141, 8388607, 1785, 33554431, 24573, 134217727, 1905, 536870911, 651, 2147483647
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OFFSET
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1,2
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COMMENT
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Since n -> 2^n - 1 is an embedding of the ordered structure N = {1, 2, 3, ...} (the order being the "divides" relation) into itself, A064084(n) always divides A000225(n); the sequence of quotients of A000225 and A064084 is A064085.
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FORMULA
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A064084(n) := (2^((p_1)^(e_1)) - 1) * ... * (2^((p_k)^(e_k)) - 1) where (p_1)^(e_1) * ... * (p_k)^(e_k) is the prime factorization of n.
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EXAMPLE
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A064084(6) = (2^2 - 1) * (2^3 - 1) = 21 since 6 = 2 * 3.
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CROSSREFS
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Cf. A000225, A064085, A064086.
Sequence in context: A062544 A120411 A069112 this_sequence A090633 A098583 A043729
Adjacent sequences: A064081 A064082 A064083 this_sequence A064085 A064086 A064087
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KEYWORD
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mult,easy,nonn
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AUTHOR
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Jens Voss (jens.voss(AT)poet.de), Sep 04 2001
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