A180615 Numbers starting with 1 such that the sum of any two distinct elements has an odd number of distinct prime factors.

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

Author

Michel Lagneau, Jan 21 2011

Keywords

• nonn

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, ...

Examples

			The set {6, 58, 124} gives the number of distinct prime factors {1, 3, 3}.
		

Crossrefs

Cf. A180514.

Programs

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

Extensions

a(23)-a(30) from Donovan Johnson, Jan 25 2011