OFFSET
1,1
COMMENTS
This sequence contains numbers k in A126706 for which A376846(k) = 0; A376846(k) = 0 for prime powers k or squarefree numbers k (i.e., k in A303554).
It is sufficient to determine floor(log k / log p) <= Omega(k) for p = lpf(k) = A020639(k).
Sequence contains numbers k of the form 2^j*3, j > 1, i.e., A007283 \ {3, 6} is a proper subset of this sequence, since 2^(j+1) < 2^j*3 and j+1 = Omega(2^j*3).
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
Michael De Vlieger, Numbers k for which floor(log k / log lpf(k)) <= bigomega(k), 2024.
EXAMPLE
12 is in the sequence since 2^3 < 12, and Omega(2^3) = Omega(12) = 3.
20 is not in the sequence since 2^4 < 20 and Omega(2^4) = 4, but Omega(20) = 3.
45 is in the sequence since 3^3 < 45, and Omega(3^3) = Omega(45) = 3.
375 = 3*5^3 is not in the sequence since 3^5 < 375 and Omega(3^5) = 5, but Omega(345) = 4.
MATHEMATICA
Select[Select[Range[4000], Nor[PrimePowerQ[#], SquareFreeQ[#]] &], Function[{n, k}, NoneTrue[FactorInteger[n][[All, 1]], Floor@ Log[#, n] > k &]] @@ {#, PrimeOmega[#]} &] ]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Michael De Vlieger, Nov 02 2024
STATUS
approved