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A006939 Chernoff sequence: a(n) = Product_{k=1..n} prime(k)^(n-k+1).
(Formerly M2050)
38
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) = prod(j=1..n, A002110(n) ).

Superprimorials, from primorials by analogy with superfactorials.

Smallest number with n distinct exponents in its prime factorization.

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

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

KEYWORD

easy,nonn,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

Corrected and extended by Labos Elemer, May 30 2001

STATUS

approved

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Last modified August 20 03:34 EDT 2017. Contains 290823 sequences.