OFFSET
1,22
COMMENTS
Number of m not exceeding n such that the squarefree kernel of m divides n, and m has more prime factors with repetition than does n.
Number of m in row n of A162306 such that Omega(m) > Omega(n).
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
Michael De Vlieger, Hasse diagrams of m in select rows n of A162306 indicating in red those m such that Omega(m) > Omega(n).
FORMULA
EXAMPLE
Table of select n such that a(n) > 0:
n a(n) List of m such that Omega(m) > Omega(n).
-------------------------------------------------
10 1 {8}
14 1 {8}
18 1 {16}
20 1 {16}
22 2 {8, 16}
26 2 {8, 16}
28 1 {16}
30 2 {16, 24}
33 1 {27}
34 3 {8, 16, 32}
36 1 {32}
38 3 {8, 16, 32}
39 1 {27}
40 1 {32}
42 4 {16, 24, 32, 36}
MATHEMATICA
rad[x_] := rad[x] = Times @@ FactorInteger[x][[All, 1]];
{0}~Join~Table[With[{k = PrimeOmega[n]}, Count[Range[n], _?(And[Divisible[n, rad[#]], PrimeOmega[#] > k] &)]], {n, 2, 120}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael De Vlieger, Oct 06 2024
STATUS
approved