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

1,2

Links

Table of n, a(n) for n=1..96.

Formula

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

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A279849 A106826 A259582 * A139048 A182101 A242289

Adjacent sequences: A377934 A377935 A377936 * A377938 A377939 A377940

Keyword

nonn

Author

Ctibor O. Zizka, Nov 11 2024

Status

approved