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A270650 Min(i, j), where p(i)*p(j) is the n-th term of A006881.

%I A270650 #11 Mar 05 2024 07:03:14
%S A270650 1,1,1,2,2,1,1,2,1,3,1,2,1,2,3,2,1,1,3,2,1,4,1,3,1,2,4,2,1,3,1,2,3,1,
%T A270650 4,1,2,2,4,1,2,1,5,3,1,3,1,2,4,1,2,1,2,3,5,1,2,1,4,3,1,5,2,1,3,4,1,2,
%U A270650 6,1,3,2,6,2,5,1,4,1,3,2,1,1,4,2,3,1
%N A270650 Min(i, j), where p(i)*p(j) is the n-th term of A006881.
%H A270650 Clark Kimberling, <a href="/A270650/b270650.txt">Table of n, a(n) for n = 1..1000</a>
%e A270650 A006881 = (6, 10, 14, 15, 21, 22, 26, 33, 34, 35, 38, ... ), the increasing sequence of all products of distinct primes.  The first 4 factorizations are 2*3, 2*5, 2*7, 3*5, so that (a(1), a(2), a(3), a(4)) = (1,1,1,2).
%t A270650 mx = 350; t = Sort@Flatten@Table[Prime[n]*Prime[m], {n, Log[2, mx/3]}, {m, n + 1, PrimePi[mx/Prime[n]]}]; (* A006881, _Robert G. Wilson v_, Feb 07 2012 *)
%t A270650 u = Table[FactorInteger[t[[k]]][[1]], {k, 1, Length[t]}];
%t A270650 u1 = Table[u[[k]][[1]], {k, 1, Length[t]}]  (* A096916 *)
%t A270650 PrimePi[u1]  (* A270650 *)
%t A270650 v = Table[FactorInteger[t[[k]]][[2]], {k, 1, Length[t]}];
%t A270650 v1 = Table[v[[k]][[1]], {k, 1, Length[t]}]  (* A070647 *)
%t A270650 PrimePi[v1]  (* A270652 *)
%t A270650 d = v1 - u1  (* A176881 *)
%t A270650 Map[PrimePi[FactorInteger[#][[1, 1]]] &, Select[Range@ 240, And[SquareFreeQ@ #, PrimeOmega@ # == 2] &]] (* _Michael De Vlieger_, Apr 25 2016 *)
%Y A270650 Cf. A000040, A006881, A096916, A070647, A270652, A270003.
%K A270650 nonn,easy
%O A270650 1,4
%A A270650 _Clark Kimberling_, Apr 25 2016