A082049 Least composite number greater than n-th composite number having greater smallest prime factor than that of n-th composite number.

9, 9, 9, 25, 15, 15, 15, 25, 21, 21, 21, 25, 25, 25, 49, 27, 35, 33, 33, 33, 35, 35, 49, 39, 39, 49, 45, 45, 45, 49, 49, 49, 121, 51, 55, 55, 55, 77, 57, 65, 63, 63, 63, 65, 65, 77, 69, 69, 77, 75, 75, 75, 77, 77, 121, 81, 81, 85, 85, 85, 91, 87, 91, 91, 91, 121, 93, 95, 95

Offset: 1

Author

Reinhard Zumkeller, Apr 02 2003

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002808, A020639, A056608.

Programs

Mathematica

seq[lim_] := Module[{c = Select[Range[lim], CompositeQ], p, s = {}, n, v}, p = FactorInteger[#][[1, 1]] & /@ c; n = Length[p]; Do[v = 0; Do[If[p[[j]] > p[[i]], v = c[[j]]; Break[]], {j, i + 1, n}]; If[v == 0, Break[], AppendTo[s, v]], {i, 1, n}]; s]; seq[125] (* Amiram Eldar, Mar 26 2025 *)

Formula

A020639(a(n)) > A020639(A002808(n)).

A082048(A002808(n)) <= a(n).