A377792 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Permutation of A377713.

Proper subset of A120944.

LINKS

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

EXAMPLE

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

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

CROSSREFS

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

Sequence in context: A063466 A377713 A138109 * A332877 A357325 A362211

Adjacent sequences: A377789 A377790 A377791 * A377793 A377794 A377795

KEYWORD

nonn,tabf,easy,new

AUTHOR

Michael De Vlieger, Nov 07 2024

STATUS

approved