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A180615
Numbers starting with 1 such that the sum of any two distinct elements has an odd number of distinct prime factors.
3
1, 2, 3, 6, 58, 124, 254, 309, 519, 1029, 1179, 1569, 1986, 3795, 10008, 31133, 39260, 76772, 126798, 190293, 613553, 873413, 1324947, 16893137, 23186977, 65348522, 91513433, 168375480, 836588442, 844570409
OFFSET
1,2
COMMENTS
Numbers starting with 4 :
4, 5, 12, 25, 85, 126, 145, 186, 252, 1146, ...
Numbers starting with 5 :
5, 6, 11, 26, 55, 424, 444, 589, 722, 1573, ...
Numbers starting with 7 :
7, 9, 10, 20, 22, 118, 350, 1012, 1433, 2043, ...
EXAMPLE
The set {6, 58, 124} gives the number of distinct prime factors {1, 3, 3}.
MAPLE
with(numtheory):nn:=1000000:T:=array(1..nn): U:=array(1..nn): for p from 1
to nn do: T[p]:=p:U[p]:=1:od:for u from 1 to 30 do: k:=1+u:for n from u+1 to
nn do:s:=T[n]+T[u]:s1:=nops(factorset(s)):z:=irem(s1, 2):if z=1 then U[k]:=T[n]:k:=k+1:else
fi:od:for i from 1 to nn do:T[i]:=U[i]:od:od:for j from 1 to 30 do:printf(`%d, `, T[j]):od:
MATHEMATICA
t={1}; k=1; Do[k++; While[! And @@ OddQ[Length /@ FactorInteger[t+k]], k++]; AppendTo[t, k], {10}]; t
CROSSREFS
Cf. A180514.
Sequence in context: A062309 A018390 A307104 * A018409 A226933 A018415
KEYWORD
nonn
AUTHOR
Michel Lagneau, Jan 21 2011
EXTENSIONS
a(23)-a(30) from Donovan Johnson, Jan 25 2011
STATUS
approved