A243289 n minus the index of the greatest prime dividing n-th squarefree number: a(n) = n - A243290(n).

1, 1, 1, 1, 3, 2, 4, 3, 3, 6, 8, 5, 5, 10, 10, 7, 11, 8, 16, 9, 16, 15, 19, 12, 17, 20, 14, 24, 15, 21, 16, 25, 17, 29, 27, 26, 20, 20, 28, 34, 36, 23, 34, 40, 25, 25, 35, 43, 43, 28, 38, 29, 46, 40, 45, 32, 51, 47, 44, 52, 36, 36, 56, 37, 61, 50, 39, 39, 64, 58

Offset: 1

Author

Antti Karttunen, Jun 03 2014

Keywords

• nonn

Comments

If A005117(n) <= 2n, or equally, if A243351 is always positive, then this sequence is certainly positive as well.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005117, A006530, A049084, A243290, A243291, A243348, A243349, A243351.

Programs

Mathematica

With[{t = Table[PrimePi[FactorInteger[k][[-1, 1]]], {k, Select[Range[120], SquareFreeQ]}]}, Range[Length[t]] - t] (* Amiram Eldar, Mar 04 2024 *)

Formula

a(n) = n - A243290(n).