A163644 - OEIS

A163644

Product of primes which do not exceed n and do not divide the swinging factorial n$ (A056040).

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).

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Peter Luschny, Die schwingende Fakultät und Orbitalsysteme, August 2011.

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:

MATHEMATICA

A034386[x_] := Apply[Times, Table[Prime[w], {w, 1, PrimePi[x]}]];

sf[n_] := With[{f = Floor[n/2]}, Pochhammer[f + 1, n - f]/f!];

A163641[0] = 1; A163641[n_] := Times @@ FactorInteger[sf[n]][[All, 1]]; Join[{1}, Table[A034386[n]/A163641[n], {n, 1, 50}]] (* G. C. Greubel, Aug 01 2017 *)

CROSSREFS

Cf. A056040, A034386, A163641, A056610.

Sequence in context: A123073 A059289 A201277 * A339901 A290348 A014465

Adjacent sequences: A163641 A163642 A163643 * A163645 A163646 A163647

KEYWORD

nonn

AUTHOR

Peter Luschny, Aug 02 2009

STATUS

approved