A073855 Number of steps to reach 0 starting with n and applying the process x ->bigomega(x), where bigomega = A001222.

0, 1, 2, 2, 3, 2, 3, 2, 3, 3, 3, 2, 3, 2, 3, 3, 4, 2, 3, 2, 3, 3, 3, 2, 4, 3, 3, 3, 3, 2, 3, 2, 3, 3, 3, 3, 4, 2, 3, 3, 4, 2, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 2, 4, 3, 4, 3, 3, 2, 4, 2, 3, 3, 4, 3, 3, 2, 3, 3, 3, 2, 3, 2, 3, 3, 3, 3, 3, 2, 3, 4, 3, 2, 4, 3, 3, 3, 4, 2, 4, 3, 3, 3, 3, 3, 4, 2, 3, 3, 4, 2, 3, 2, 4, 3

Offset: 0

Author

Benoit Cloitre, Sep 02 2002

Keywords

• easy
• nonn

Examples

			bigomega(36) = 4, bigomega(4) = 2, bigomega(2) = 1, bigomega(1) = 0, hence a(36) = 4.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..10000
• Index entries for sequences computed from exponents in factorization of n

Crossrefs

Cf. A001222, A036430.

Programs

Maple

A073855 := proc(n)
    option remember;
    if n <=0 then
        0;
    else
        1+procname(numtheory[bigomega](n)) ;
    end if;
end proc:
seq(A073855(n),n=0..20) ; # R. J. Mathar, Jul 31 2017

Mathematica

Table[-1 + Length@ NestWhileList[PrimeOmega, n, # > 0 &], {n, 0, 105}] (* Michael De Vlieger, Jul 29 2017 *)

PARI

a(n)=if(n<=0,0,s=n; c=1; while(bigomega(s)>0,s=bigomega(s); c++); c)

PARI

A073855(n) = if(!n,n,1+A073855(bigomega(n))); \\ Antti Karttunen, Jul 28 2017

PARI

first(n) = my(v = vector(n-1)); v[1] = 1; for(i=2, #v, v[i] = 1 + v[bigomega(i)]); concat([0], v) \\ David A. Corneth, Jul 28 2017

Formula

a(n) = 1+A036430(n).

For n >= 1, a(n) = 1 + a(bigomega(n)). - Vladeta Jovovic, Jul 10 2004

With a(0) = 0 as the termination condition of the recurrence. - Antti Karttunen, Jul 28 2017

Extensions

More terms from Vladeta Jovovic, Jul 10 2004

Term a(0)=0 prepended by Antti Karttunen, Jul 28 2017