A376847 Number of m > n such that rad(m) | n and Omega(m) <= Omega(n), where rad = A007947 and Omega = A001222.
0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 1, 0, 0, 1, 0, 3, 1, 1, 0, 4, 0, 1, 0, 3, 0, 4, 0, 0, 1, 1, 1, 2, 0, 1, 1, 5, 0, 5, 0, 3, 2, 1, 0, 6, 0, 1, 1, 3, 0, 1, 1, 5, 1, 1, 0, 11, 0, 1, 2, 0, 1, 5, 0, 3, 1, 5, 0, 4, 0, 1, 1, 3, 1, 5, 0, 8, 0, 1, 0, 11, 1, 1, 1
Offset: 1
Keywords
Examples
Table of select n such that a(n) > 0:
n a(n) List of m in A376248 such that Omega(m) <= Omega(n)
-------------------------------------------------------------
6 1 {9}
10 1 {25}
12 2 {18, 27}
14 1 {49}
15 1 {25}
18 1 {27}
20 3 {25, 50, 125}
24 4 {27, 36, 54, 81}
28 3 {49, 98, 343}
30 4 {45, 50, 75, 125}
40 5 {50, 100, 125, 250, 625}
48 6 {54, 72, 81, 108, 162, 243}
60 11 {75, 81, 90, 100, 125, 135, 150, 225, 250, 375, 625}
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..10000
- Michael De Vlieger, Hasse diagrams of m in select R(n), where R(n) is the union of rows n of A162306 and A376248, indicating in blue those m > n such that Omega(m) <= Omega(n).
Programs
-
Maple
with(NumberTheory): cond := (m, n) -> irem(n, Radical(m)) = 0 and Omega(m) <= Omega(n): a := n -> nops(select(m -> cond(m, n), [seq(n+1..A068795(n))])): seq(a(n), n = 1..87); # Peter Luschny, Oct 25 2024
-
Mathematica
rad[x_] := rad[x] = Times @@ FactorInteger[x][[All, 1]]; Table[k = PrimeOmega[n]; w = PrimeNu[n]; Binomial[k + w, w] - Count[Range[n], _?(And[Divisible[n, rad[#]], PrimeOmega[#] > k] &)], {n, 120}]