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A369419
Numbers k that are neither squarefree nor prime powers such that A119288(k) <= k/A007947(k) < A053669(k) and A007947(k) is not a primorial.
2
18, 90, 150, 630, 1050, 1470, 1890, 2100, 6930, 11550, 16170, 20790, 23100, 25410, 90090, 150150, 210210, 270270, 300300, 330330, 390390, 420420, 450450, 1531530, 2552550, 3573570, 4594590, 5105100, 5615610, 6636630, 7147140, 7657650, 8678670, 9189180, 29099070
OFFSET
1,1
LINKS
FORMULA
This sequence is { k = m*P(i) : 3 <= m < prime(i), i > 1, m in A369361 }.
Intersection of A364998 and A056808.
EXAMPLE
Seen as an irregular triangle T(n,k) of rows n where T(n,k) = P(n)*k, and k < prime(n+1) is in A369361.
n\k 3 5 7 9 10 11
------------------------------------------------
2: 18;
3: 90, 150;
4: 630, 1050, 1470, 1890, 2100;
5: 6930, 11550, 16170, 20790, 23100, 25410;
...
MATHEMATICA
P = 2; nn = 8;
s = Select[Range[3, Prime[nn+1]],
Nor[IntegerQ@ Log2[#],
And[EvenQ[#1], Union@ Differences@ PrimePi[#2[[All, 1]]] == {1},
AllTrue[Differences@ #2[[All, -1]], # <= 0 &]]] & @@
{#, FactorInteger[#]} &];
Table[P *= Prime[n]; P*TakeWhile[s, # < Prime[n + 1] &], {n, 2, nn}]
KEYWORD
nonn
AUTHOR
Michael De Vlieger, Mar 10 2024
STATUS
approved