A069230 Number of primes p such that n < p < n + tau(n)^2 where tau(n) = A000005(n).

0, 2, 1, 3, 1, 5, 0, 5, 3, 5, 1, 10, 0, 4, 4, 6, 1, 9, 0, 8, 3, 4, 0, 14, 2, 4, 4, 9, 1, 14, 0, 8, 4, 4, 4, 19, 0, 4, 4, 15, 1, 14, 0, 8, 8, 4, 0, 19, 1, 8, 3, 8, 0, 14, 3, 14, 4, 5, 1, 29, 0, 3, 7, 11, 4, 13, 0, 8, 4, 13, 1, 27, 0, 3, 8, 8, 3, 13, 0, 19, 5, 3, 0, 26, 2, 3, 3, 13, 0, 27, 3, 7, 4, 5, 5

Offset

1,2

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Example

a(12) = 10 as there are 10 primes between (exclusive) 12 and 12 + tau(12)^2 = 12 + 6^2 = 12 + 36 = 48 namely the 10 primes 13, 17, 19, 23, 29, 31, 37, 41, 43, 47. - David A. Corneth, Sep 20 2020

Mathematica

Table[Count[Range[n+1, n+DivisorSigma[0, n]^2-1], _?PrimeQ], {n, 100}] (* Harvey P. Dale, Oct 25 2021 *)

Prog

(PARI) a(n) = #select(x->isprime(x), vector(numdiv(n)^2-1, k, k+n)); \\ Michel Marcus, Jun 18 2017

Crossrefs

Cf. A000005, A069231, A069232, A069233.

Sequence in context: A325642 A110977 A295785 * A349348 A242180 A163961

Adjacent sequences: A069227 A069228 A069229 * A069231 A069232 A069233

Keyword

nonn,easy

Author

Benoit Cloitre, Apr 13 2002

Status

approved