OFFSET
1,6
COMMENTS
This sequence has the same relationship to A001221 as A000523 has to A001222. Also, for n>=1, n-1 occurs as A002110(n)-A002110(n-1) consecutive terms beginning with term a(A002110(n-1)), where A002110 is the primorials; i.e. the frequencies of occurrence are the first differences (1,4,24,180,...) of the primorials.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..65536
Safia Aoudjit and Djamel Berkane, Explicit Estimates Involving the Primorial Integers and Applications, J. Int. Seq., Vol. 24 (2021), Article 21.7.8.
EXAMPLE
a(7)=2 because omega(1)=0, omega(2)=omega(3)=omega(4)=omega(5)=omega(7)=1 and omega(6)=2 (as 6=2*3), so 2 is the maximum.
MAPLE
a:= proc(n) option remember; `if`(n=0, 0,
max(a(n-1), nops(ifactors(n)[2])))
end:
seq(a(n), n=1..105); # Alois P. Heinz, Aug 19 2021
MATHEMATICA
FoldList[Max, PrimeNu /@ Range[105]] (* Michael De Vlieger, Dec 29 2021 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Rick L. Shepherd, Aug 24 2005
STATUS
approved