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.

6, 15, 21, 35, 55, 65, 85, 95, 115, 385, 455, 595, 77, 91, 119, 133, 161, 203, 217, 259, 287, 301, 329, 1001, 1309, 1463, 1547, 1729, 1771, 2093, 2233, 2261, 2387, 143, 187, 209, 253, 319, 341, 407, 451, 473, 517, 583, 649, 671, 737, 781, 803, 869, 913, 979, 1067

Offset: 1

Author

Michael De Vlieger, Nov 07 2024

Keywords

• nonn
• tabf
• easy

Comments

Permutation of A377713.

Proper subset of A120944.

Examples

			Let b(n) = A377793(n).
In A377713, there are terms k with smallest prime factor prime(n) as follows:
    Prime(n)  | b(n) | k such that floor(log_lpf(k) k) <= Omega(k)
-------------------------------------------------------------------------------
prime(1) =  2 |   1  | 6
prime(2) =  3 |   2  | 15, 27
prime(3) =  5 |   9  | 35, 55, 65, 85, 95, 115, 385, 455, 595
prime(4) =  7 |  21  | 77, 91, 119, 133, 161, 203, 217, 259, 287, 301, 329, 1001,
              |      | 1309, 1463, 1547, 1729, 1771, 2093, 2233, 2261, 2387
prime(5) = 11 | 128  | 143, 187, 209, ..., 1733303
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..16116 (rows n = 1..10, flattened)

Crossrefs

Cf. A001222, A020639, A120944, A377713, A377793.

Programs

Mathematica

Table[p = Prime[i]; m = p^3;
  Set[{w, t}, {{p, NextPrime[p]}, False}];
  Union@ Reap[
    Do[Set[s, Times @@ w];
      If[s < m,
        AppendTo[w, NextPrime@ Last[w]]; m *= p; Sow[s],
        If[Length[w] < 3, Break[],
          w = Append[w[[;; -3]], NextPrime@ w[[-2]] ]; m /= p] ],
      Infinity] ][[-1, 1]], {i, 10}] // Flatten