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A163644 Product of primes which do not exceed n and do not divide the swinging factorial n$ (A056040). 0
1, 1, 1, 1, 1, 1, 3, 3, 3, 1, 5, 5, 5, 5, 35, 7, 7, 7, 21, 21, 105, 5, 55, 55, 165, 33, 429, 143, 1001, 1001, 1001, 1001, 1001, 91, 1547, 221, 221, 221, 4199, 323, 323, 323, 2261, 2261, 24871, 24871, 572033, 572033, 572033, 81719, 408595, 24035, 312455 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

a(n) = primorial(n) / rad(n$) = A034386(n) / A163641(n).

REFERENCES

Peter Luschny, "Divide, swing and conquer the factorial and the lcm{1,2,...,n}", preprint, April 2008.

LINKS

Table of n, a(n) for n=0..52.

Peter Luschny, Swinging Factorial.

EXAMPLE

a(20) = 105 because in the prime-factorization of 20$ the primes 3, 5 and 7 are missing and 3*5*7 = 105.

MAPLE

a := proc(n) local p; mul(p, p=select(isprime, {$1..n})

minus numtheory[factorset](n!/iquo(n, 2)!^2)) end:

CROSSREFS

Cf. A056040, A034386, A163641, A056610.

Sequence in context: A123073 A059289 A201277 * A014465 A226645 A243095

Adjacent sequences:  A163641 A163642 A163643 * A163645 A163646 A163647

KEYWORD

nonn

AUTHOR

Peter Luschny, Aug 02 2009

STATUS

approved

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Last modified March 27 06:50 EDT 2017. Contains 284144 sequences.