A369541 - OEIS

%I #9 Feb 03 2024 09:53:37

%S 24,120,180,840,1260,1680,9240,13860,18480,27720,120120,180180,240240,

%T 360360,480480,2042040,3063060,4084080,6126120,8168160,38798760,

%U 58198140,77597520,116396280,155195040,892371480,1338557220,1784742960,2677114440,3569485920,5354228880

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

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

%H Michael De Vlieger, <a href="/A369541/b369541.txt">Table of n, a(n) for n = 1..10000</a>

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

%F Intersection of A364998 and A025487.

%e Seen as an irregular triangle T(n,k) of rows n where P(n) | T(n,k)

%e 2:      24;

%e 3:     120,     180;

%e 4:     840,    1260,    1680;

%e 5:    9240,   13860,   18480,   27720;

%e 6:  120120,  180180,  240240,  360360,  480480;

%e 7: 2042040, 3063060, 4084080, 6126120, 8168160;

%e    ...

%t P = 2; nn = 10;

%t  s = Select[Range[4, Prime[nn], 2],

%t    Or[IntegerQ@ Log2[#],

%t      And[Union@ Differences@ PrimePi[#1] == {1},

%t         AllTrue[Differences[#2], # <= 0 &]] & @@

%t         Transpose@ FactorInteger[#]] &];

%t  Table[P *= Prime[n];

%t    P*TakeWhile[s, # <= Prime[n + 1] &], {n, 2, nn}] // Flatten

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

%K nonn

%O 1,1

%A _Michael De Vlieger_, Jan 28 2024