A082926 Difference between the number of primes equal to or less than n and (1 + the number of nonsquarefree numbers equal to or less than n).

1, 0, 1, 0, 1, 1, 2, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 2, 3, 2, 2, 1, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 1, 2, 3, 3, 2, 3, 4, 5, 5, 6, 5, 6, 6, 7, 7, 7, 6, 7, 6, 6, 7, 8, 8, 8, 7, 8, 8, 8, 7, 8, 7, 7, 8, 9, 9, 9, 8, 9, 10, 10, 9, 10, 10, 10, 10, 11, 10, 11, 11, 12, 12, 12, 12, 13, 12

Offset: 1

Author

Anonymous, Apr 15 2003

Keywords

• nonn

Links

• Jinyuan Wang, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000720, A057627.

Programs

Mathematica

nsfQ[n_] := n == 1 || ! SquareFreeQ[n]; Abs[Accumulate[Table[If[nsfQ[n], 1, 0] - If[PrimeQ[n], 1, 0], {n, 1, 100}]]] (* Amiram Eldar, Jun 13 2022 *)

PARI

a(n) = abs(sum(k=1, n, !issquarefree(k)) + 1 - primepi(n)); \\ Michel Marcus, Mar 27 2020

Formula

a(n) = abs(A057627(n) + 1 - A000720(n)). - Michel Marcus, Mar 27 2020

Extensions

Name edited by Michel Marcus, Jun 14 2022