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A171157 Number of distinct primes > 3 that divide n.

%I A171157 #10 Nov 16 2024 14:09:12
%S A171157 0,0,0,0,1,0,1,0,0,1,1,0,1,1,1,0,1,0,1,1,1,1,1,0,1,1,0,1,1,1,1,0,1,1,
%T A171157 2,0,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,0,2,1,1,1,1,1,1,1,1,0,2,1,1,1,
%U A171157 1,2,1,0,1,1,1,1,2,1,1,1,0,1,1,1,2,1,1,1,1,1,2,1,1,1,2,0,1,1,1,1,1,1,1,1,2
%N A171157 Number of distinct primes > 3 that divide n.
%H A171157 G. C. Greubel, <a href="/A171157/b171157.txt">Table of n, a(n) for n = 1..10000</a>
%F A171157 a(n) = A001221(n) - A171182(n).
%p A171157 omega := proc(n) nops(numtheory[factorset](n)) ; end proc:
%p A171157 A171182 := proc(n) op(1+ (n mod 6),[2,0,1,1,1,0]) ; end proc:
%p A171157 A171157 := proc(n) omega(n)-A171182(n) ; end proc: seq(A171157(n),n=1..120) ; # _R. J. Mathar_, Dec 09 2009
%t A171157 Table[PrimeNu[n] - (5 + 3*Cos[n*Pi] + 4*Cos[2*n*Pi/3])/6, {n, 1, 100}] (* _G. C. Greubel_, May 16 2017 *)
%t A171157 Table[Count[FactorInteger[n][[;;,1]],_?(#>3&)],{n,110}] (* _Harvey P. Dale_, Nov 16 2024 *)
%o A171157 (PARI) for(n=1,100, print1(round(omega(n) - (5 + 3*cos(n*Pi) + 4*cos(2*n*Pi/3))/6), ", ")) \\ _G. C. Greubel_, May 16 2017
%Y A171157 Cf. A001221, A171182.
%K A171157 nonn
%O A171157 1,35
%A A171157 _Juri-Stepan Gerasimov_, Dec 04 2009