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
Examples
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
Links
- David A. Corneth, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
Table[Count[Range[n+1,n+DivisorSigma[0,n]^2-1],?PrimeQ],{n,100}] (* _Harvey P. Dale, Oct 25 2021 *)
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PARI
a(n) = #select(x->isprime(x), vector(numdiv(n)^2-1, k, k+n)); \\ Michel Marcus, Jun 18 2017