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A369540
Numbers k neither squarefree nor prime powers such that A119288(k) <= k/A007947(k) < A053669(k) and A007947(k) is a primorial P(i) = A002110(i) for some i.
3
18, 24, 90, 120, 150, 180, 630, 840, 1050, 1260, 1470, 1680, 1890, 2100, 6930, 9240, 11550, 13860, 16170, 18480, 20790, 23100, 25410, 27720, 90090, 120120, 150150, 180180, 210210, 240240, 270270, 300300, 330330, 360360, 390390, 420420, 450450, 480480, 1531530
OFFSET
1,1
COMMENTS
Nonsquarefree numbers k such that omega(k) > 1, whose squarefree kernel rad(k) is a primorial, with second least prime factor not greater than k/rad(k), and k/rad(k) is smaller than the smallest nondivisor prime.
Definition implies the following:
1.) A119288(k) = 3 since all terms are even, hence 6 | k.
2.) k is a product m * P(n), n > 1, such that rad(m) | P(n) and 3 <= m < prime(n+1).
Superset of A369541.
LINKS
FORMULA
{a(n)} = { m × P(n) : 3 <= m < q, n >= 2 }.
Intersection of A364998 and A055932.
A060735 without primorials P(i) and 2*P(i).
EXAMPLE
Seen as a table T(n,k) of rows n where P(n) | T(n,k)
2: 18, 24;
3: 90, 120, 150, 180;
4: 630, 840, 1050, 1260, 1470, 1680, 1890, 2100;
5: 6930, 9240, 11550, 13860, 16170, 18480, 20790, 23100, 25410, 27720;
...
12 is not in the sequence since 3 <= 12/6 < 5 is false.
18 is in the sequence since 3 <= 18/6 < 5 is true.
36 is not in the sequence since 3 <= 36/6 < 5 is false.
Generally, 2*P(i) is not in the sequence since 3 <= 2*P(i)/P(i) < prime(i+1) is false.
MATHEMATICA
P = 2; Table[P *= Prime[n]; Array[# P &, Prime[n + 1] - 3, 3], {n, 2, 6}] // Flatten
KEYWORD
nonn,easy
AUTHOR
Michael De Vlieger, Jan 28 2024
STATUS
approved