A083720 Product of the primes less than the greatest prime factor of n but not dividing n.

1, 1, 2, 1, 6, 1, 30, 1, 2, 3, 210, 1, 2310, 15, 2, 1, 30030, 1, 510510, 3, 10, 105, 9699690, 1, 6, 1155, 2, 15, 223092870, 1, 6469693230, 1, 70, 15015, 6, 1, 200560490130, 255255, 770, 3, 7420738134810, 5, 304250263527210, 105, 2, 4849845

Offset

1,3

Comments

a(n) is squarefree, and all squarefree numbers appear infinitely often. a(m) = a(n) if and only if rad(m) = rad(n), where rad is A007947. - Charles R Greathouse IV, Apr 09 2024

Links

Michael De Vlieger, Table of n, a(n) for n = 1..2376

Formula

a(n) = A002110(A049084(A006530(n)))/A007947(n).

a(A000040(k)) = A002110(k-1).

a(n) = 1 iff n = m*A002110(k) and A006530(m) <= A000040(k).

Mathematica

Array[Times @@ Complement[Prime@ Range@ PrimePi@ Last[#], #] &[FactorInteger[#][[All, 1]]] &, 46] (* Michael De Vlieger, Apr 09 2024 *)

Crossrefs

Cf. A079067, A083722.

See the formula section for the relationships with A000040, A002110, A006530, A007947, A049084.

Sequence in context: A173279 A277440 A321597 * A369925 A055878 A331654

Adjacent sequences: A083717 A083718 A083719 * A083721 A083722 A083723

Keyword

nonn,easy,changed

Author

Reinhard Zumkeller, May 04 2003

Extensions

Edited by Peter Munn, Apr 09 2024

Status

approved