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

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

filter:= n -> nops(select(isprime, [$(n+1) .. (n+numtheory:-tau(n)^2-1)]))=3:
select(filter, [$1..1000]); # Robert Israel, Jan 05 2018

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 *)

Prog

(PARI) isok(n) = #select(x->isprime(x), vector(numdiv(n)^2-1, k, k+n)) == 3; \\ Michel Marcus, Jun 18 2017

Crossrefs

Cf. A000005, A049591, A069230, A069232, A069233.

Sequence in context: A132750 A297296 A048582 * A243635 A243636 A243637

Adjacent sequences: A069228 A069229 A069230 * A069232 A069233 A069234

Keyword

easy,nonn

Author

Benoit Cloitre, Apr 13 2002

Status

approved