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

1,7

Links

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

Formula

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

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 *)

Prog

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

Crossrefs

Cf. A000720, A057627.

Sequence in context: A330961 A345236 A321223 * A060564 A031267 A247763

Adjacent sequences: A082923 A082924 A082925 * A082927 A082928 A082929

Keyword

nonn

Author

Anonymous, Apr 15 2003

Extensions

Name edited by Michel Marcus, Jun 14 2022

Status

approved