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

Author

Reinhard Zumkeller, May 04 2003

Keywords

• nonn
• easy

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

Rad(n*a(n)) = A002110(A000720(A006530(n))) is the smallest primorial number divisible by rad(n). - David James Sycamore, May 15 2024

Links

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

Crossrefs

Cf. A079067, A083722.

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

Programs

Mathematica

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

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).

Extensions

Edited by Peter Munn, Apr 09 2024