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

1,3

Links

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

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A002110 (primorial numbers).

Sequence in context: A327454 A124655 A338219 * A228151 A276087 A341837

Adjacent sequences: A066835 A066836 A066837 * A066839 A066840 A066841

Keyword

nonn

Author

Leroy Quet, Jan 20 2002

Status

approved