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%I #23 Mar 28 2021 07:01:45
%S 0,1,1,2,1,2,1,3,2,1,1,3,1,1,2,4,1,3,1,2,2,1,1,4,2,1,3,2,1,2,1,5,1,1,
%T 2,4,1,1,1,3,1,2,1,2,3,1,1,5,2,1,1,2,1,4,2,3,1,1,1,3,1,1,3,6,2,2,1,2,
%U 1,1,1,5,1,1,3,2,2,2,1,4,4,1,1,3,2,1,1,3,1,3,2,2,1,1,2,6,1,1,2,2,1,2,1,3,3,1,1,5,1,1,1,4,1,2,2,2,2,1,2,4
%N a(n) = number of prime factors of n that are < the square of smallest prime factor of n (counted with multiplicity), a(1) = 0.
%H Antti Karttunen, <a href="/A284257/b284257.txt">Table of n, a(n) for n = 1..10001</a>
%F a(n) = A001222(A284255(n)).
%F a(n) = A001222(n) - A284256(n).
%e For n = 45 = 3*3*5, all prime factors 3, 3 and 5 are less than 3^2, thus a(45) = 3.
%e For n = 120 = 2*2*2*3*5, the prime factors less than 2^2 are 2*2*2*3, thus a(120) = 4.
%t Table[If[n == 1, 0, Count[#, d_ /; d < First[#]^2] &@ Flatten@ Map[ConstantArray[#1, #2] & @@ # &, FactorInteger@ n]], {n, 120}] (* _Michael De Vlieger_, Mar 24 2017 *)
%o (Scheme) (define (A284257 n) (A001222 (A284255 n)))
%o (PARI) A(n) = if(n<2, return(1), my(f=factor(n)[, 1]); for(i=2, #f, if(f[i]>f[1]^2, return(f[i]))); return(1));
%o a(n) = if(A(n)==1, 1, A(n)*a(n/A(n)));
%o for(n=1, 150, print1(bigomega(n/a(n)),", ")) \\ _Indranil Ghosh_, Mar 24 2017, after _David A. Corneth_
%o (Python)
%o from sympy import primefactors
%o def Omega(n): return 0 if n==1 else Omega(n//min(primefactors(n))) + 1
%o def A(n):
%o pf = primefactors(n)
%o if pf: min_pf2 = min(pf)**2
%o for i in pf:
%o if i > min_pf2: return i
%o return 1
%o def a(n): return 1 if A(n)==1 else A(n)*a(n//A(n))
%o print([Omega(n//a(n)) for n in range(1, 151)]) # _Indranil Ghosh_, Mar 24 2017
%Y Cf. A001222, A020639, A284252, A284253, A284254, A284256, A284258, A284259.
%K nonn
%O 1,4
%A _Antti Karttunen_, Mar 24 2017
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