A069231 Numbers n such that there are exactly 3 primes p satisfying the inequality n < p < n + tau(n)^2 where tau(n) = A000005(n).
4, 9, 21, 51, 55, 62, 74, 77, 82, 86, 87, 91, 106, 122, 123, 129, 134, 142, 143, 145, 146, 155, 158, 159, 161, 177, 183, 214, 215, 217, 237, 249, 254, 259, 265, 274, 278, 298, 299, 301, 309, 334, 335, 339, 341, 343, 358, 365, 371, 377, 382, 386, 394, 395, 407
Offset: 1
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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Maple
filter:= n -> nops(select(isprime, [$(n+1) .. (n+numtheory:-tau(n)^2-1)]))=3: select(filter, [$1..1000]); # Robert Israel, Jan 05 2018
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Mathematica
fQ[n_] := Block[{r = Range[n, n + DivisorSigma[0, n]^2]}, If[ PrimeQ@ n, r = Rest@ r]; If[ PrimeQ[ r[[-1]]], r = Most@ r]; Length@ Select[r, PrimeQ] == 3]; Select[Range@410, fQ] (* Robert G. Wilson v, Jan 05 2018 *) -
PARI
isok(n) = #select(x->isprime(x), vector(numdiv(n)^2-1, k, k+n)) == 3; \\ Michel Marcus, Jun 18 2017