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A377792 Irregular triangle where row n lists squarefree composite k with lpf(k) = prime(n) such that m <= Omega(k), where lpf = A020639, m = floor(log k / log lpf(k)), and Omega = A001222.

%I A377792 #9 Nov 13 2024 17:17:38
%S A377792 6,15,21,35,55,65,85,95,115,385,455,595,77,91,119,133,161,203,217,259,
%T A377792 287,301,329,1001,1309,1463,1547,1729,1771,2093,2233,2261,2387,143,
%U A377792 187,209,253,319,341,407,451,473,517,583,649,671,737,781,803,869,913,979,1067
%N A377792 Irregular triangle where row n lists squarefree composite k with lpf(k) = prime(n) such that m <= Omega(k), where lpf = A020639, m = floor(log k / log lpf(k)), and Omega = A001222.
%C A377792 Permutation of A377713.
%C A377792 Proper subset of A120944.
%H A377792 Michael De Vlieger, <a href="/A377792/b377792.txt">Table of n, a(n) for n = 1..16116</a> (rows n = 1..10, flattened)
%e A377792 Let b(n) = A377793(n).
%e A377792 In A377713, there are terms k with smallest prime factor prime(n) as follows:
%e A377792     Prime(n)  | b(n) | k such that floor(log_lpf(k) k) <= Omega(k)
%e A377792 -------------------------------------------------------------------------------
%e A377792 prime(1) =  2 |   1  | 6
%e A377792 prime(2) =  3 |   2  | 15, 27
%e A377792 prime(3) =  5 |   9  | 35, 55, 65, 85, 95, 115, 385, 455, 595
%e A377792 prime(4) =  7 |  21  | 77, 91, 119, 133, 161, 203, 217, 259, 287, 301, 329, 1001,
%e A377792               |      | 1309, 1463, 1547, 1729, 1771, 2093, 2233, 2261, 2387
%e A377792 prime(5) = 11 | 128  | 143, 187, 209, ..., 1733303
%t A377792 Table[p = Prime[i]; m = p^3;
%t A377792   Set[{w, t}, {{p, NextPrime[p]}, False}];
%t A377792   Union@ Reap[
%t A377792     Do[Set[s, Times @@ w];
%t A377792       If[s < m,
%t A377792         AppendTo[w, NextPrime@ Last[w]]; m *= p; Sow[s],
%t A377792         If[Length[w] < 3, Break[],
%t A377792           w = Append[w[[;; -3]], NextPrime@ w[[-2]] ]; m /= p] ],
%t A377792       Infinity] ][[-1, 1]], {i, 10}] // Flatten
%Y A377792 Cf. A001222, A020639, A120944, A377713, A377793.
%K A377792 nonn,tabf,easy
%O A377792 1,1
%A A377792 _Michael De Vlieger_, Nov 07 2024