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

%I A369541 #9 Feb 03 2024 09:53:37
%S A369541 24,120,180,840,1260,1680,9240,13860,18480,27720,120120,180180,240240,
%T A369541 360360,480480,2042040,3063060,4084080,6126120,8168160,38798760,
%U A369541 58198140,77597520,116396280,155195040,892371480,1338557220,1784742960,2677114440,3569485920,5354228880
%N A369541 Numbers k neither squarefree nor prime powers that are products of primorials such that A119288(k) <= k/A007947(k) < A053669(k).
%C A369541 Proper subset of A369540, itself contained in A060735, which in turn is a subset of A055932.
%H A369541 Michael De Vlieger, <a href="/A369541/b369541.txt">Table of n, a(n) for n = 1..10000</a>
%F A369541 {a(n)} = { m × P(n) : 3 <= m < q, n >= 2, m not in A025487 }.
%F A369541 Intersection of A364998 and A025487.
%e A369541 Seen as an irregular triangle T(n,k) of rows n where P(n) | T(n,k)
%e A369541 2:      24;
%e A369541 3:     120,     180;
%e A369541 4:     840,    1260,    1680;
%e A369541 5:    9240,   13860,   18480,   27720;
%e A369541 6:  120120,  180180,  240240,  360360,  480480;
%e A369541 7: 2042040, 3063060, 4084080, 6126120, 8168160;
%e A369541    ...
%t A369541 P = 2; nn = 10;
%t A369541  s = Select[Range[4, Prime[nn], 2],
%t A369541    Or[IntegerQ@ Log2[#],
%t A369541      And[Union@ Differences@ PrimePi[#1] == {1},
%t A369541         AllTrue[Differences[#2], # <= 0 &]] & @@
%t A369541         Transpose@ FactorInteger[#]] &];
%t A369541  Table[P *= Prime[n];
%t A369541    P*TakeWhile[s, # <= Prime[n + 1] &], {n, 2, nn}] // Flatten
%Y A369541 Cf. A002110, A007947, A025487, A053669, A055932, A060735, A119288, A364998, A369540.
%K A369541 nonn
%O A369541 1,1
%A A369541 _Michael De Vlieger_, Jan 28 2024