A351436 a(n) = n - A351168(n).

0, 1, 1, 3, 1, 2, 1, 7, 5, 2, 1, 4, 1, 2, 3, 15, 1, 10, 1, 4, 3, 2, 1, 8, 9, 2, 19, 4, 1, 6, 1, 31, 3, 2, 5, 20, 1, 2, 3, 8, 1, 6, 1, 4, 9, 2, 1, 16, 13, 18, 3, 4, 1, 38, 5, 8, 3, 2, 1, 12, 1, 2, 9, 63, 5, 6, 1, 4, 3, 10, 1, 40, 1, 2, 27, 4, 7, 6, 1, 16, 65, 2

Offset: 1

Author

Ben Polson, Feb 11 2022

Keywords

• nonn

Crossrefs

Cf. A351168, A006530 (largest prime factor), A071178 (exponent).

Programs

Mathematica

a[n_] := n - Module[{f = FactorInteger[n]}, n*(1 - 1/f[[-1, 1]])^f[[-1, 2]]]; a[1] = 0; Table[a[n], {n, 2, 83}] (* Robert P. P. McKone, Feb 11 2022, from Amiram Eldar in A351168 *)

Formula

a(n) = n * (1 - ((A006530(n) - 1)/A006530(n))^A071178).