A377937 - OEIS

%I #20 Nov 13 2024 16:36:39

%S 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,

%T 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,

%U 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

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

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

%e n = 1, there is one prime in [0, 2], thus a(1) = 1.

%e n = 6, there are four primes in [2, 10], thus a(6) = 4.

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

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

%K nonn

%O 1,2

%A _Ctibor O. Zizka_, Nov 11 2024