A369541 Numbers k neither squarefree nor prime powers that are products of primorials such that A119288(k) <= k/A007947(k) < A053669(k).

24, 120, 180, 840, 1260, 1680, 9240, 13860, 18480, 27720, 120120, 180180, 240240, 360360, 480480, 2042040, 3063060, 4084080, 6126120, 8168160, 38798760, 58198140, 77597520, 116396280, 155195040, 892371480, 1338557220, 1784742960, 2677114440, 3569485920, 5354228880

Offset: 1

Author

Michael De Vlieger, Jan 28 2024

Keywords

• nonn

Comments

Proper subset of A369540, itself contained in A060735, which in turn is a subset of A055932.

Examples

			Seen as an irregular triangle T(n,k) of rows n where P(n) | T(n,k)
2:      24;
3:     120,     180;
4:     840,    1260,    1680;
5:    9240,   13860,   18480,   27720;
6:  120120,  180180,  240240,  360360,  480480;
7: 2042040, 3063060, 4084080, 6126120, 8168160;
   ...
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002110, A007947, A025487, A053669, A055932, A060735, A119288, A364998, A369540.

Programs

Mathematica

P = 2; nn = 10;
 s = Select[Range[4, Prime[nn], 2],
   Or[IntegerQ@ Log2[#],
     And[Union@ Differences@ PrimePi[#1] == {1},
        AllTrue[Differences[#2], # <= 0 &]] & @@
        Transpose@ FactorInteger[#]] &];
 Table[P *= Prime[n];
   P*TakeWhile[s, # <= Prime[n + 1] &], {n, 2, nn}] // Flatten

Formula

{a(n)} = { m × P(n) : 3 <= m < q, n >= 2, m not in A025487 }.

Intersection of A364998 and A025487.