OFFSET
1,1
COMMENTS
Numbers k such that Omega(k) > omega(k) > 1 with all prime power factors p^m for m > 1, such that squarefree kernel rad(k) is in A002110, where Omega = A001222, omega = A001221, and rad(k) = A007947(k).
Union of the product of the squares of primorials P(n)^2, n > 1, and the set of prime(n)-smooth numbers.
Superset of A364930.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
FORMULA
EXAMPLE
This sequence is the union of the following infinite sets:
P(2)^2 * A003586 = {36, 72, 108, 144, 216, 288, 324, ...}
= { m*P(2)^2 : rad(m) | P(2) }.
P(3)^2 * A051037 = {900, 1800, 2700, 3600, 4500, 5400, ...}
= { m*P(3)^2 : rad(m) | P(3) }.
P(4)^2 * A002473 = {44100, 88200, 132300, 176400, ...}
= { m*P(4)^2 : rad(m) | P(4) }, etc.
MATHEMATICA
With[{nn = 2^14},
Select[
Select[Rest@ Union@ Flatten@ Table[a^2*b^3, {b, nn^(1/3)}, {a, Sqrt[nn/b^3]}],
Not@*PrimePowerQ],
And[EvenQ[#],
Union@ Differences@ PrimePi[FactorInteger[#][[All, 1]]] == {1}] &] ]
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael De Vlieger, Jan 22 2024
STATUS
approved