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A083720
Product of the primes less than the greatest prime factor of n but not dividing n.
11
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
Rad(n*a(n)) = A002110(A000720(A006530(n))) is the smallest primorial number divisible by rad(n). - David James Sycamore, May 15 2024
LINKS
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
See the formula section for the relationships with A000040, A002110, A006530, A007947, A049084.
Sequence in context: A173279 A277440 A321597 * A369925 A055878 A331654
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, May 04 2003
EXTENSIONS
Edited by Peter Munn, Apr 09 2024
STATUS
approved