A377937 Number of primes in the interval [n - A000005(n), n + A000005(n)].

1, 2, 3, 4, 3, 4, 2, 3, 2, 3, 2, 4, 2, 3, 4, 4, 2, 4, 2, 3, 3, 2, 1, 5, 1, 2, 3, 3, 2, 4, 2, 3, 3, 2, 2, 5, 1, 2, 3, 4, 2, 4, 2, 3, 3, 2, 1, 4, 1, 2, 2, 2, 1, 4, 2, 3, 3, 2, 2, 5, 2, 2, 3, 4, 2, 5, 1, 3, 3, 3, 2, 6, 2, 2, 3, 3, 2, 4, 1, 5, 2, 2, 1, 4, 2, 2, 2, 2, 1, 5, 1, 2, 2, 1, 1, 5

Offset: 1

Author

Ctibor O. Zizka, Nov 11 2024

Keywords

• nonn

Examples

			n = 1, there is one prime in [0, 2], thus a(1) = 1.
n = 6, there are four primes in [2, 10], thus a(6) = 4.
		

Crossrefs

Cf. A000005, A000040, A000720, A049820, A062249.

Programs

Mathematica

a[n_] := Module[{d = DivisorSigma[0, n]}, PrimePi[n + d] - PrimePi[n - d - 1]]; Array[a, 100] (* Amiram Eldar, Nov 11 2024 *)

Formula

a(n) = pi(n+tau(n)) - pi(n-tau(n)-1).