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

1,2

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, ...

Links

Table of n, a(n) for n=1..30.

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

Adjacent sequences: A180612 A180613 A180614 * A180616 A180617 A180618

Keyword

nonn

Author

Michel Lagneau, Jan 21 2011

Extensions

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

Status

approved