A073752 Greatest common divisor of n/spf(n) and n/gpf(n) where spf(n) is the smallest and gpf(n) is the greatest prime factor of n (see A020639, A006530).

1, 1, 1, 2, 1, 1, 1, 4, 3, 1, 1, 2, 1, 1, 1, 8, 1, 3, 1, 2, 1, 1, 1, 4, 5, 1, 9, 2, 1, 3, 1, 16, 1, 1, 1, 6, 1, 1, 1, 4, 1, 3, 1, 2, 3, 1, 1, 8, 7, 5, 1, 2, 1, 9, 1, 4, 1, 1, 1, 6, 1, 1, 3, 32, 1, 3, 1, 2, 1, 5, 1, 12, 1, 1, 5, 2, 1, 3, 1, 8, 27, 1, 1, 6, 1, 1, 1, 4, 1, 9, 1, 2, 1, 1, 1, 16, 1, 7, 3, 10, 1

Offset: 1

Author

Reinhard Zumkeller, Aug 07 2002

Keywords

• nonn

Comments

a(n) = if n=p^k (p prime, k>0) then p^(k-1) else n/(spf(n)*gpf(n)).

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000961, A066048.

A073753(n) = a(a(n)).

Programs

Mathematica

gc[n_]:=Module[{fi=Transpose[FactorInteger[n]][[1]]},GCD[n/First[fi], n/Last[ fi]]]; Array[gc,110] (* Harvey P. Dale, Jun 17 2012 *)

Formula

a(n) = GCD(A032742(n), A052126(n)).