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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).
3
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
1,1
COMMENTS
Proper subset of A369540, itself contained in A060735, which in turn is a subset of A055932.
LINKS
FORMULA
{a(n)} = { m X P(n) : 3 <= m < q, n >= 2, m not in A025487 }.
Intersection of A364998 and A025487.
EXAMPLE
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;
...
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
KEYWORD
nonn
AUTHOR
Michael De Vlieger, Jan 28 2024
STATUS
approved