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

1,1

Comments

A073484(a(n)) = 1.

Links

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A269703 A057487 A073486 * A325161 A175586 A089995

Adjacent sequences: A073484 A073485 A073486 * A073488 A073489 A073490

Keyword

nonn

Author

Reinhard Zumkeller, Aug 03 2002

Status

approved