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A006939
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Chernoff sequence: a(n) = Product_{k=1..n} prime(k)^(n-k+1).
(Formerly M2050)
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29
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1, 2, 12, 360, 75600, 174636000, 5244319080000, 2677277333530800000, 25968760179275365452000000, 5793445238736255798985527240000000, 37481813439427687898244906452608585200000000, 7517370874372838151564668004911177464757864076000000000, 55784440720968513813368002533861454979548176771615744085560000000000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Product of first n primorials: a(n)=Product[A002110(n)],j=1..n.
Superprimorials, from primorials by analogy with superfactorials.
Smallest number with n distinct exponents in its prime factorization.
Subsequence of A130091. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 06 2007
Hankel transform of A171448. [From Paul Barry (pbarry(AT)wit.ie), Dec 09 2009]
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REFERENCES
| C. Pickover, Mazes for the Mind, St. Martin's Press, NY, 1992, p. 351.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..25
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FORMULA
| a(n) = m(1)*m(2)*m(3)*...*m(n), where m(n) = n-th primorial number. [njas, Feb 20 2005]
a(0) = 1, a(n) = a(n - 1)p(n)#, where p(n)# is the n-th primorial (the product of the first n primes). [Alonso del Arte, Sep 30 2011]
log a(n) = n^2(log n + log log n - 3/2 + o(1))/2. [Charles R Greathouse IV, Mar 14 2011]
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EXAMPLE
| a(4) = 360 because 2^3 * 3^2 * 5 = 1 * 2 * 6 * 30 = 360.
a(5) = 75600 because 2^4 * 3^3 * 5^2 * 7 = 1 * 2 * 6 * 30 * 210 = 75600.
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MAPLE
| a := []; printlevel := -1; for k from 1 to 20 do a := [op(a), product(ithprime(i)^(k-i+1), i=1..k)] od; print(a);
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MATHEMATICA
| Rest[FoldList[Times, 1, FoldList[Times, 1, Prime[Range[15]]]]] (* From Harvey P. Dale, Jul 07 2011 *)
Table[Times@@Table[Prime[i]^(n - i + 1), {i, n}], {n, 12}] (* From Alonso del Arte, Sep 30 2011 *)
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PROG
| (PARI) a(n)=prod(k=1, n, prime(k)^(n-k+1)) \\ Charles R Greathouse IV, Jul 25 2011
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CROSSREFS
| Cf. A000178 (product of first n factorials), A007489 (sum of first n factorials), A060389 (sum of first n primorials).
Cf. A002110, A051357.
Sequence in context: A061307 A061300 A079264 * A152686 A131690 A158261
Adjacent sequences: A006936 A006937 A006938 * A006940 A006941 A006942
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KEYWORD
| easy,nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Corrected and extended by Labos E. (labos(AT)ana.sote.hu), May 30 2001
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