A382768 Number of k < n that are coprime to n and neither squarefree nor prime powers.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 0, 3, 0, 3, 0, 1, 0, 5, 0, 5, 0, 2, 0, 3, 0, 6, 0, 2, 0, 7, 0, 7, 0, 2, 1, 9, 0, 9, 0, 5, 1, 12, 0, 8, 1, 7, 1, 14, 0, 15, 1, 5, 2, 10, 0, 16, 2, 8, 0, 17, 0, 18, 2, 5, 3, 16, 0, 20, 1, 10, 3, 21, 0

Offset: 1

Author

Michael De Vlieger, Apr 04 2025

Keywords

• nonn
• easy

Comments

Let s = A126706, the set of numbers that are neither squarefree nor prime powers.

Let q(k) be the number of terms in A126706 that do not exceed k. For example, q(20) = 3, since s(1..3) = {12, 18, 20}.

a(n) = 0 for n < A382248(n). Only 72 numbers n are such that a(n) = 0, with n = 2310 the largest n such that a(n) = 0.

a(A002110(k)) = 0 for k < 6.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002110, A073311, A126706, A139555, A382248.

Programs

Magma

nn := 120; q := 1; t := []; res := []; for n in [1..nn] do if not IsSquarefree(n) and not IsPrimePower(n) then Append(~t, n); q +:= 1; end if; c := 0; for i in [1..#t] do if GCD(t[i], n) eq 1 then c +:= 1; end if; end for; Append(~res, c); end for; res; // Vincenzo Librandi, Apr 22 2025

Mathematica

nn = 120; q = 1; Table[Set[{c, i}, {0, 1}]; If[Nor[SquareFreeQ[n], PrimePowerQ[n]], t[q] = n; q++]; While[i < q, If[CoprimeQ[t[i], n], c++]; i++]; c, {n, nn}]