cp's OEIS Frontend

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

%I A180615 #9 Mar 30 2012 18:35:54
%S A180615 1,2,3,6,58,124,254,309,519,1029,1179,1569,1986,3795,10008,31133,
%T A180615 39260,76772,126798,190293,613553,873413,1324947,16893137,23186977,
%U A180615 65348522,91513433,168375480,836588442,844570409
%N A180615 Numbers starting with 1 such that the sum of any two distinct elements has an odd number of distinct prime factors.
%C A180615 Numbers starting with 4 :
%C A180615 4, 5, 12, 25, 85, 126, 145, 186, 252, 1146, ...
%C A180615 Numbers starting with 5 :
%C A180615 5, 6, 11, 26, 55, 424, 444, 589, 722, 1573, ...
%C A180615 Numbers starting with 7 :
%C A180615 7, 9, 10, 20, 22, 118, 350, 1012, 1433, 2043, ...
%e A180615 The set {6, 58, 124} gives the number of distinct prime factors {1, 3, 3}.
%p A180615 with(numtheory):nn:=1000000:T:=array(1..nn): U:=array(1..nn): for p from 1
%p A180615   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
%p A180615   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
%p A180615   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:
%t A180615 t={1}; k=1; Do[k++; While[! And @@ OddQ[Length /@ FactorInteger[t+k]], k++]; AppendTo[t, k], {10}]; t
%Y A180615 Cf. A180514.
%K A180615 nonn
%O A180615 1,2
%A A180615 _Michel Lagneau_, Jan 21 2011
%E A180615 a(23)-a(30) from _Donovan Johnson_, Jan 25 2011