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 A006939 Chernoff sequence: a(n) = Product_{k=1..n} prime(k)^(n-k+1). (Formerly M2050) 60
 1, 2, 12, 360, 75600, 174636000, 5244319080000, 2677277333530800000, 25968760179275365452000000, 5793445238736255798985527240000000, 37481813439427687898244906452608585200000000, 7517370874372838151564668004911177464757864076000000000, 55784440720968513813368002533861454979548176771615744085560000000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Product of first n primorials: a(n) = Product_{i=1..n} A002110(i). Superprimorials, from primorials by analogy with superfactorials. Smallest number k with n distinct exponents in its prime factorization, i.e., A071625(k) = n. Subsequence of A130091. - Reinhard Zumkeller, May 06 2007 Hankel transform of A171448. - Paul Barry, Dec 09 2009 This might be a good place to explain the name "Chernoff sequence" since his name does not appear in the References or Links as of Mar 22 2014. - Jonathan Sondow, Mar 22 2014 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). LINKS T. D. Noe, Table of n, a(n) for n=0..25 FORMULA a(n) = m(1)*m(2)*m(3)*...*m(n), where m(n) = n-th primorial number. - N. J. A. Sloane, 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 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. MAPLE a := []; printlevel := -1; for k from 0 to 20 do a := [op(a), product(ithprime(i)^(k-i+1), i=1..k)] od; print(a); MATHEMATICA Rest[FoldList[Times, 1, FoldList[Times, 1, Prime[Range[15]]]]] (* Harvey P. Dale, Jul 07 2011 *) Table[Times@@Table[Prime[i]^(n - i + 1), {i, n}], {n, 12}] (* Alonso del Arte, Sep 30 2011 *) PROG (PARI) a(n)=prod(k=1, n, prime(k)^(n-k+1)) \\ Charles R Greathouse IV, Jul 25 2011 (Haskell) a006939 n = a006939_list !! n a006939_list = scanl1 (*) a002110_list -- Reinhard Zumkeller, Jul 21 2012 (MAGMA) [1] cat [(&*[NthPrime(k)^(n-k+1): k in [1..n]]): n in [1..15]]; // G. C. Greubel, Oct 14 2018 CROSSREFS Cf. A000178 (product of first n factorials), A007489 (sum of first n factorials), A060389 (sum of first n primorials). Cf. A002110, A051357. Cf. A001221 (second omega or number of distinct prime factors), A001222 (first omega or number of prime factors with multiplicity), A059404 (third omega is > 1), A062770 (third omega is 1), A071625 (third omega, or number of distinct exponents in prime factorization), A118914 (prime signature), A181819, A181821, A182857 (smallest number > 1 with n omegas), A323014 (length of omega-sequence), A323023 (k-th omega of n). Sequence in context: A061307 A061300 A079264 * A152686 A131690 A158261 Adjacent sequences:  A006936 A006937 A006938 * A006940 A006941 A006942 KEYWORD easy,nonn,nice AUTHOR EXTENSIONS Corrected and extended by Labos Elemer, May 30 2001 STATUS approved

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Last modified June 7 05:20 EDT 2020. Contains 334837 sequences. (Running on oeis4.)