A393471 - OEIS

%I #36 Mar 25 2026 20:35:26

%S 2,6,30,10,14,42,66,22,26,78,102,34,38,190,70,210,330,33,3,15,105,21,

%T 35,385,55,5,65,195,39,91,546,462,110,230,46,69,138,114,57,95,285,255,

%U 51,85,170,130,182,406,58,87,174,186,62,93,930,510,1122,2310,2590,74

%N The radical value of the product of adjacent terms of A392505.

%C For n <= 2^14, the only primes in the sequence are {2, 3, 5, 11}. Apart from 2, these primes are followed by their squares in A393471. These may be the only primes in this sequence. - _Michael De Vlieger_, Mar 24 2026

%H Scott R. Shannon, <a href="/A393471/b393471.txt">Table of n, a(n) for n = 1..10000</a>

%H Michael De Vlieger, <a href="/A393471/a393471.png">Log log scatterplot of a(n)</a>, n = 1..2^14, showing primes in red and squarefree composites in other colors. Terms in yellow are even squarefree semiprimes and terms in light green are odd squarefree semiprimes, appearing in two increasingly well defined trajectories near the bottom of the graph.

%H Scott R. Shannon, <a href="/A393471/a393471_1.png">Image of the first 100000 terms</a>.

%F a(n) = A007947(A392505(n)*A392505(n+1)). - _Michael De Vlieger_, Mar 24 2026

%t Block[{c, q}, nn = 120; c[_] := False; q[_] := False; Set[{i, j}, {1, 2}]; u = 3; MapIndexed[Set[{c[#], q[#]}, {True, True}] &, {1, 2}]; rad[x] := Times @@ FactorInteger[x][[All, 1]]; {i, j}~Join~Reap[Do[If[PrimePowerQ[j], p = FactorInteger[j][[1, 1]]; k = 1; While[Or[c[#], q[rad[j*#] ] ] &[p*k], k++]; k *= p, k = u; While[Or[c[k], q[rad[j*k] ], CoprimeQ[j, k] ], k++] ]; Sow[rad[j*k] ]; Set[{q[rad[j*k] ], c[k], i, j}, {True, True, j, k}]; If[k == u, While[c[u], u++]], {n, 3, nn}] ][[-1, 1]] ] (* _Michael De Vlieger_, Mar 24 2026 *)

%Y Cf. A392505, A007947, A005117, A046388, A100484, A120944.

%K nonn,look

%O 1,1

%A _Scott R. Shannon_, Mar 24 2026