A393471 The radical value of the product of adjacent terms of A392505.

2, 6, 30, 10, 14, 42, 66, 22, 26, 78, 102, 34, 38, 190, 70, 210, 330, 33, 3, 15, 105, 21, 35, 385, 55, 5, 65, 195, 39, 91, 546, 462, 110, 230, 46, 69, 138, 114, 57, 95, 285, 255, 51, 85, 170, 130, 182, 406, 58, 87, 174, 186, 62, 93, 930, 510, 1122, 2310, 2590, 74

Offset

1,1

Comments

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

Links

Scott R. Shannon, Table of n, a(n) for n = 1..10000

Michael De Vlieger, Log log scatterplot of a(n), 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.

Scott R. Shannon, Image of the first 100000 terms.

Formula

a(n) = A007947(A392505(n)*A392505(n+1)). - Michael De Vlieger, Mar 24 2026

Mathematica

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 *)

Crossrefs

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

Sequence in context: A079615 A076978 A117213 * A394417 A394422 A127797

Adjacent sequences: A393468 A393469 A393470 * A393472 A393473 A393474

Keyword

nonn,look

Author

Scott R. Shannon, Mar 24 2026

Status

approved