A066838 Product of primes < n that do not divide n.

1, 1, 2, 3, 6, 5, 30, 105, 70, 21, 210, 385, 2310, 2145, 2002, 15015, 30030, 85085, 510510, 969969, 461890, 440895, 9699690, 37182145, 44618574, 8580495, 74364290, 15935205, 223092870, 215656441, 6469693230, 100280245065

Offset: 1

Author

Leroy Quet, Jan 20 2002

Keywords

• nonn

Examples

			a(8) = 105 = 3 * 5 * 7 because 3, 5 and 7 are the primes < 8 that do not divide 8.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..2350

Crossrefs

Cf. A002110 (primorial numbers).

Programs

Maple

Primes:= select(isprime, [$2..100]):
seq(convert(select(t -> t <= n and n mod t <> 0, Primes),`*`), n=1..100); # Robert Israel, Jun 19 2016

Mathematica

Table[Apply[Times, Select[Prime@ Range@ PrimePi@ n, CoprimeQ[#, n] &] /. {} -> 1], {n, 32}] (* or *)
Table[E^Sum[(1 - Floor[n/k] + Floor[(n - 1)/k]) Boole@ PrimeQ[k] MangoldtLambda@ k, {k, 2, n}], {n, 32}] (* Michael De Vlieger, Jun 22 2016 *)
Table[Times@@Complement[Prime[Range[PrimePi[n]]],FactorInteger[n][[All,1]]],{n,40}] (* Harvey P. Dale, Feb 05 2022 *)

PARI

a(n) = prod(i=1, n-1, if (isprime(i) && (n%i) , i, 1)); \\ Michel Marcus, May 20 2014

Formula

a(prime(n)) = A002110(n-1). - Michel Marcus, May 20 2014

a(n) = e^[Sum_{k=2..n} (1-floor(n/k)+floor((n-1)/k))*A010051(k)*M(k)] where M(n) is the Mangoldt function. - Anthony Browne, Jun 17 2016