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A073487
Squarefree numbers having exactly one prime gap.
6
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
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
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Aug 03 2002
STATUS
approved