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Search: id:A061149
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| A061149 |
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Smallest number whose number of divisors = n-th primorial (A002110). |
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5
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| 2, 12, 720, 907200, 251475840000, 14272938808128000000, 1683176415906545239680000000000, 216212806227686567939021962996416000000000000
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Beyond the 4-th term these are only conjectures.
The n-th term is divisible by the product of first n primorial numbers (A006939(n)), the n-th Chernoff-number. Also the numbers are refactorable (A033950).
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FORMULA
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The n-th term is constructed as a product of special powers of the first n prime, as follows: a(n)=Product[ p(j)^[p(n-j+1)-1] ], j=1...n
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EXAMPLE
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a(1)=2 a(2)=(2^2)*(3^1)=12, a(3)=(2^4)*(3^2)*(5^1)=720 .... a(7)=(2^16)*(3^12)*(5^10)*(7^6)*(11^4)*(13^2)*(17^1)= 1683176415906545239680000000000. a(7) is divisible with the product of the first 7 primorial numbers(=A006939(7)): a(7)/2677277333530800000=628689600000.
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CROSSREFS
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Cf. A002110, A006939, A000005, A005179, A033950.
Sequence in context: A052129 A141770 A060055 this_sequence A129933 A064320 A112373
Adjacent sequences: A061146 A061147 A061148 this_sequence A061150 A061151 A061152
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KEYWORD
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nice,nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), May 30 2001
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