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A064084
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A multiplicative version of 2^n - 1 (A000225).
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3
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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, 4294967295, 14329, 393213, 3937, 7665, 137438953471, 1572861, 57337
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OFFSET
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1,2
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COMMENTS
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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, a(n) always divides A000225(n); the sequence of quotients of A000225 and a is A064085.
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LINKS
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FORMULA
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a(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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a(6) = (2^2 - 1) * (2^3 - 1) = 21 since 6 = 2 * 3.
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MAPLE
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a:= n-> mul(2^(i[1]^i[2])-1, i=ifactors(n)[2]):
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MATHEMATICA
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a[n_] := Times @@ (2^(Power @@@ FactorInteger[n]) - 1); Array[a, 40] (* Amiram Eldar, Aug 31 2023 *)
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PROG
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(PARI) a(n) = my(f=factor(n)); for (i=1, #f~, f[i, 1] = 2^(f[i, 1]^f[i, 2])-1; f[i, 2]=1); factorback(f); \\ Michel Marcus, Jun 09 2014
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CROSSREFS
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KEYWORD
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mult,easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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