A073487 Squarefree numbers having exactly one prime gap.

10, 14, 21, 22, 26, 33, 34, 38, 39, 42, 46, 51, 55, 57, 58, 62, 65, 66, 69, 70, 74, 78, 82, 85, 86, 87, 91, 93, 94, 95, 102, 106, 111, 114, 115, 118, 119, 122, 123, 129, 133, 134, 138, 141, 142, 145, 146, 154, 155, 158, 159, 161, 165, 166, 174, 177, 178, 183, 185

Offset: 1

Author

Reinhard Zumkeller, Aug 03 2002

Keywords

• nonn

Comments

A073484(a(n)) = 1.

Examples

			78 is a term, as 78 = 2*3*13 with one gap between 3 and 13.
		

Links

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

Crossrefs

Cf. A005117, A073486, A073488, A073489, A073493.

Programs

Maple

N:= 1000: # to get all terms <= N
Res:= NULL:
for a from 1 to numtheory:-pi(isqrt(N)) do
  for b from a do
    p:= mul(ithprime(i),i=a..b);
    if p > N/ithprime(b+2) then break fi;
    for c from b+2 while p*ithprime(c) <= N do
      for d from c do
        q:= mul(ithprime(i),i=c..d);
        if p*q > N then break fi;
        Res:= Res, p*q;
      od
    od
  od
od:
sort([Res]); # Robert Israel, Apr 20 2017

Mathematica

okQ[n_] := SquareFreeQ[n] && Length[SequencePosition[FactorInteger[n][[All, 1]], {p_?PrimeQ, q_?PrimeQ} /; q != NextPrime[p]]] == 1;
Select[Range[200], okQ] (* Jean-François Alcover, Feb 28 2019 *)